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Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road

New Delhi – 110 018, Ph. : 9312629035, 8527112111

MT – 1

TRIGONOMETRY

Sy l labus :

Trigonometrical identities and equations.Trigonometric functions. Inverse trigonometricalfunctions and their properties. Height and Distances.


New Delhi – 110 018, Ph. : 9312629035, 8527112111

MT – 2

C O N C E P T S

Trogonometric Identities & Ratios

C1 Basic Trigonometric Identities :

(a) sin2 + cos2 = 1; –1 sin 1; –1 cos 1 R

(b) sec2 – tan2 = 1; |sec | 1 R –

In,2

)1n2(

(c) cosec2 – cot2 = 1 ; |cosec | 1 R – {n, n I}

Practice Problems :

1. The value of cos2 50 + cos2 100 + ...... cos2 850 + cos2 900 will be

(a)2

17(b)

2

19(c) 1 (d) 0

(a)

2. If sec – tan = k then the value of cos will be

(a)1k

k22

(b)1k

k22

(c)k2

1k 2 (d)

k2

1k 2

(a)

3. If cosec A + cot A = 2

11 then tan A equals

(a)22

21(b)

16

15(c)

117

44(d)

43

117

(c)

[Answers : (1) a (2) a (3) c]

C2 Trigonometric Functions Of Allied Angles :

If is any angle, then –, 90 ± , 180 ± , 270 ± , 360 ± etc. are called Allied Angles.

(a) sin (–) = –sin ; cos (–) = cos

(b) sin (900 – ) = cos ; cos (900 – ) = sin

(c) sin (900 + ) = cos ; cos (900 + ) = – sin

(d) sin (1800 – ) = sin ; cos (1800 – ) = – cos

(e) sin (1800 + ) = – sin ; cos (1800 + ) = – cos

(f) sin (2700 – ) = – cos ; cos (2700 – ) = – sin

(g) sin (2700 + ) = – cos ; cos (2700 + ) = sin

(h) tan (900 – ) = cot ; cot (900 – ) = tan

Practice Problems :

1. If 2

1sin and is obtuse then cot equals

(a)3

1(b)

3

1 (c) 3 (d) 3

2. The value of sin 100 + sin 200 + sin 300......sin 3600 is

(a) 0 (b) 1 (c) –1 (d) none of these


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MT – 3

3. The value of cos 10 . cos 20 . cos 30.......cos 1800 will be

(a) 0 (b) 1

(c) 100 (d) cannot be found

4. The value of cos 10 + cos 20 + cos 30.......cos 1800 will be

(a) 0 (b) –1 (c) 1 (d) none of these

5. The value of log [cos 10 + cos 20 + cos 30 ..... cos 1800] will be

(a) 0 (b) 1 (c) –1 (d) not defined

6. The value of log [cot 10 . cot 20 . cot 30 ..... cot 890] will be

(a) 0 (b) 1 (c) –1 (d) not defined

[Answers : (1) d (2) a (3) a (4) b (5) d (6) a]

C3 Trigonometric Functions of Sum of Difference of Two Angles :

(a) sin (A ± B) = sinA cosB ± cosA sin B

(b) cos (A ± B) = cosA cosB sinA sin B

(c) sin2A – sin2B = cos2B – cos2A = sin (A + B) . sin (A – B)

(d) cos2A – sin2B = cos2B – sin2A = cos (A + B) . cos (A – B)

(e)BtanAtan1

BtanAtan)BAtan(

(f)AcotBcot

1BcotAcot)BAcot(

(g)AtanCtanCtanBtanBtanAtan1

CtanBtanAtan–CtanBtanAtan)CBAtan(

Practice Problems :

1. If sin A + cos B = a and sin B + cos A = b then the value of sin (A + B) will be

(a) a2 + b2 (b)2

ba 22 (c)

2

2ba 22 (d)

2

2ba 22

2. If tan ( + ) = 2

1 and tan ( – ) =

3

1 then tan 2 will be

(a) 0 (b) 1 (c) –1 (d) none of these

3. If tan = 2

1 and tan =

3

1 then will be

(a) 0 (b)4

(c)

2

(d)

6

4. The value of cos2 480 – sin2 120 equals to

(a)4

15 (b)

4

15 (c)

8

15 (d)

8

15

5. The value of 3 cosec 200 – sec 200 is equal to

(a) 2 (b) 0

0

40sin

20sin2(c) 4 (d) 0

0

40sin

20sin4


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MT – 4

6. The value of tan 5x . tan 3x . tan 2x is equal to

(a) tan 5x – tan 3x – tan 2x (b)x2cosx3cosx5cos

x2sinx3sinx5sin

(c) 0 (d) none of these

7. The value of 00

00

9sin9cos

9sin9cos

equal to

(a) tan 540 (b) tan 360 (c) tan 180 (d) none of these

8. If A + B + C = (A, B, C > 0) and the angle C is obtuse then

(a) tan A . tan B > 1 (b) tan A . tan B < 1

(c) tan A . tan B = 1 (d) none of these

[Answers : (1) c (2) b (3) b (4) c (5) c (6) a (7) a (8) b]

C4A Factorisation of the Sum of Difference of Two Sines or Cosines :

(a)2

DCcos

2

DCsin2DsinCsin

(b)2

DCsin

2

DCcos2DsinCsin

(c)2

DCcos

2

DCcos2DcosCcos

(d)2

DCsin

2

DCsin2DcosCcos

C4B Transformation of Products into Sum of Difference of Sines & Cosines :

(a) 2sinA cosB = sin(A + B) + sin(A – B)

(b) 2cosA sinB = sin (A + B) – sin(A – B)

(c) 2 cos A cos B = cos (A + B) + cos (A – B)

(d) 2 sin A sin B = cos (A – B) – cos (A + B)

C4C Multiple and Sub-multiple Angles :

(a) sin2A = 2sinA cosA; sin = 2

cos2

sin2

(b) cos2A = cos2A – sin2A = 2cos2A – 1 = 1 – 2 sin2A; 2 cos2

2

= 1 + cos ,

2 sin2

2

= 1 – cos .

(c)

2tan1

2tan2

tan;Atan1

Atan2A2tan

22

(d)Atan1

Atan1A2cos;

Atan1

Atan2A2sin

2

2

2

(e) sin 3A = 3 sin A – 4sin3A

(f) cos 3A = 4 cos3A – 3 cosA


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MT – 5

(g)Atan31

AtanAtan3A3tan

2

3

C4D Important Trigonometric Ratios and Formula :

4

15

5cosor36cos&

4

1518sinor

10sin 00

sin2

2sin2cos......2cos.2cos.cos

n

n1n2

Practice Problems :

1. If sin A + sin B = a and cos A + cos B = b then the value of sin (A + B) will be

(a)22 ba

ab2

(b)

22 ba

ab2

(c)

ab2

ba 22 (d)

ab2

ba 22

2. The value of 00

00

40sin70cos

40cos70sin

equal to

(a) 1 (b)3

1(c) 3 (d)

2

1

3. If BcotAcosCcos

CsinAsin

, then A, B, C are in

(a) A.P. (b) G.P. (c) H.P. (d) none of these

4. The value of

nn

BcosAcos

BsinAsin

BsinAsin

BcosAcos

equals

(a)2

BAtan2 n

(b)2

BAcot2 n

(c) 0 (d) both (b) and (c) are correct

5. The value of sin 120 . sin 240 . sin 480 . sin 840 will be

(a)8

1(b)

16

1(c)

32

1(d)

64

1

6. The value of sin 360 . sin 720 . sin 1080 . sin 1440 will be

(a)4

1(b)

16

1(c)

4

3(d)

16

5

7. The value of 8

7cos

8

5cos

8

3cos

8cos 4444

(a)2

1(b)

4

1(c)

2

3(d)

4

3

8. The value of

8

7cos1

8

5cos1

8

3cos1

8cos1 will be

(a)2

1(b)

4

1(c)

8

1(d)

16

1


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MT – 6

9. The value of

10

3sin

10sin equals to

(a)2

1(b)

2

1 (c)

4

1(d) 1

10. The value of 5

8cos.

5

4cos.

5

2cos.

5cos

will be

(a)16

1(b) 0 (c)

8

1 (d)

16

1

11. The value of 18

7sin

18

5sin

18sin

equal to

(a)2

1(b)

4

1(c)

8

1(d)

16

1

[Answers : (1) a (2) c (3) a (4) d (5) b (6) d (7) c (8) c (9) c (10) d (11) c]

C5 General Solutions of Trigonometrical Equations :

(i) If sin = sin then = n + (–1)n (n I)

(ii) If cos = cos then = 2n ± (n I)

(iii) If tan = tan then = n + (n I)

(iv) If sin2 = sin2

cos2 = cos2

tan2 = tan2

then = n ± (n I)

Practice Problems :

1. The most general value of satisfying the equation tan = –1 and cos = 2

1 is

(a)4

7n

(b)

4

7)1(n n

(c)4

7n2

(d) none of these

2. The number of solution of the given equation tan + sec = 3 where 0 < < 2 is

(a) 0 (b) 1 (c) 2 (d) 3

3. If 3(sec2 + tan2) = 5 then the general solution of is

(a)6

n2

(b)6

n

(c)3

n2

(d)3

n

4. If sin 3 = sin then the general value of is

(a)3

)1n2(,n2

(b)4

)1n2(,n

(c)3

)1n2(,n

(d) none of these

5. If tan m = tan n then then the consecutive value of will be in

(a) A.P. (b) G.P. (c) H.P. (d) none of these

6. The number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2] is

(a) 0 (b) 1 (c) 2 (d) 3


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MT – 7

7. The complete solution of the equation 7cos2x + sinxcosx – 3 = 0 is given by

(a) )In(2

n

(b) )In(4

n

(c) )In(3

4tann 1

(d)

3

4tank,

4

3n 1 (k, n I)

8. If sin + cos = 2 cos then the general value of is

(a)

4

n2 (b)

4

n2 (c)

4

n (d)

4

n

9. The general solution of the equation sin100x – cos100x = 1 is

(a) In,3

n2

(b) In,2

n2

(c) In,4

n

(d) In,3

n2

[Answers : (1) c (2) c (3) b (4) b (5) a (6) d (7) d (8) b (9) b]

Inverse Trigonometric Function :

C6 Principal Values & Domains of Inverse Trigonometric/Circular Functions :

Function Domain Range

(i) y = sin–1x where –1 x 12

y2

(ii) y = cos–1x where –1 x 1 0 y

(iii) y = tan–1x where x R2

y2

(iv) y = cosec–1x where x –1 or x 1 0y,2

y2

(v) y = sec–1x where x –1 or x 12

y;y0

(vi) y = cot–1x where x R 0 < y <

C7 Properties of Inverse Trigonometric Functions :

Property - A

(i) sin (sin–1x) = x, –1 x 1

(ii) cos (cos–1x) = x, –1 x 1

(iii) tan (tan–1x) = x, x R

(iv) cot (cot–1x) = x, x R

(v) sec (sec–1x) = x, x –1, x 1

(vi) cosec (cosec–1x) = x, x –1, x 1

Property - B

(i) sin–1 (sin x) = x,2

x2

(ii) cos–1 (cos x) = x; 0 x

(iii) tan–1 (tan x) = x,2

x2


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MT – 8

(iv) cot–1 (cot x) = x; 0 x

(v) sec–1 (sec x) = x; 0 x 2

x

(vi) cosec–1 (cosec x) = x; x 0,2

x2

Property - E

(i) 1x1,2

xcosxsin 11

(ii) Rx,2

xcotxtan 11

(iii) 1|x|,2

xsecxeccos 11

Practice Problems :

1. The value of

3

2sinsin 1 is equal to

(a)3

2(b)

3

(c)

3

2 (d)

3

(d)

2. The value of )5(sinsin 1 is equal to

(a) 2 – 5 (b) 5 – 2 (c) 5 – (d) none of these

(b)

3. The value of

2

3coscos 1 is equal to

(a)2

(b) 0 (c)

2

(d)

2

3

(a)

4. The value of

7

5tantan 1 is equal to

(a)7

2(b)

7

5(c)

7

2 (d)

7

(c)

[Answers : (1) d (2) b (3) a (4) c]


New Delhi – 110 018, Ph. : 9312629035, 8527112111

MT – 9

INITIAL STEP EXERCISE

1.

x2

3tan.

2xcos

x2

7sinx

2

3cos.

2xtan 3

when simplified reduced to :

(a) sin x cos x (b) – sin2x

(c) – sin x cos x (d) sin2x

2. If cosA + cosB + cosC = 0 = sinA + sinB + sinC, thenthe value of cos (A – B) + cos (B – C) + cos (C – A)is :

(a) 3/2 (b) –(3/2)

(c) 3/4 (d) –(3/4)

3. The exact value of 000

000

110sin50sin20sin

35sin65sin80sin96

is equal to

(a) 12 (b) 24

(c) –12 (d) 48

4. If A + B + C = , then sin A + sin B + sin C =

(a)2

Ccos

2

Bcos

2

Acos4

(b)2

Ccos

2

Bcos

2

Asin4

(c)2

Ccos

2

Bsin

2

Acos4

(d)2

Csin

2

Bcos

2

Acos4

5. The value of x satisfying the equation

2

xsin2xsin1xsin1 are wheree

n I

(a) 2n x 2(n + 1)

(b) 2n x 2n +

(c) n x n +

(d) (2n – 1) x (2n + 1)

6. If A + B + C = , then cosA + cosB + cosC =

(a)2

Csin

2

Bsin

2

Asin41

(b)2

Ccos

2

Bsin

2

Asin1

(c)2

Csin

2

Bcos

2

Asin41

(d)2

Csin

2

Bsin

2

Acos1

7. If A and B are complimentary angles, then :

(a) 22

Btan1

2

Atan1

(b) 22

Bcot1

2

Acot1

(c) 22

Beccos1

2

Asec1

(d) 22

Btan1

2

Atan1

8. If = 3 and sin = 22 ba

a

. The value of the

expression a cosec – b sec is

(a) 22 ba

1

(b) 22 ba2

(c) a + b (d) none

9. If sin2x – sin x = 1, then the value of cos2x + cos4x is

(a) 1 (b) 2


10. If cosA = tanB, cosB = tanC and cosC = tanA, then

(a) A = B = C

(b)2

15Asin

(c) sinC = 3 sin180

(d)4

15Bcos


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MT – 10

FINAL STEP EXERCISE

1. If A = cos10x + sin6x, then

(a) A 1 (b) 1/2 A 3/2

(c) 0 < A 1 (d) None of these

2. Number of solutions of the simultaneous equationy = cos x and [y] = [sin y] is

(a) 2

(b) 4

(c) 6

(d) Infinitely many

3. 1cottan2cot1

cos

cossin

cossin2

33

if :

(a)

2,0 (b)

,

2

(c)

2

3, (d)

2,

2

3

4. The number of solutions of the equation1 + sin x sin2(x/2) = 0 is

(a) 0 (b) 1

(c) 2 (d) 3

5. The number of solutions of the equation2cos x = |sin x| in [–2, 2] is

(a) 1 (b) 2

(c) 4 (d) 8

6. If < tan–1x + cot–1x + cos–1x < , then possiblevalues of and are

(a) = 0, = (b) = /2, =

(c) = /2, = 3/2 (d) None of these

7. If x11 tan x = x11 , then

sin 4x =

(a) 4x (b) x

(c) 2x (d) none of these

8. , , and are the smallest positive angles inascending order of magnitude which have theirsines equal to the positive quantity k. The value of

2sin

2sin2

2sin3

2sin4

is equal to :

(a) k12 (b) k12

(c) k2 (d) 2k

9. The value of

14

7sin

14

5sin

14

3sin

14sin

14

13sin

14

11sin

14

9sin

is

(a) 1/4 (b) 1/8

(c) 1/64 (d) 1/128

11. If x = sec – tan and y = cosec + cot then :

(a)1y

1yx

(b)

x1

x1y

(c)1y

1yx

(d) xy + x + y + 1 = 0

12. The values of x satisfying the equation

1x2tanx4tan1

x2tanx4tan

aree

(a) /4 (b) n + /4

(c) 2n + /4 (d) no value

13. The set of values ‘a’ for which the equation,cos2x + a sin x = 2a – 7 possess a solution is :

(a) (–, 2) (b) [2, 6]

(c) (6, ) (d) (–, )

14. The value of

0000

2

17tan

2

167cot

2

167tan

2

17cot is

(a) a rational number

(b) 2(3 – 23)

(c) 2(3 + 3)

(d) none of these

15. If cos(sin x) = 1/2, then x may be in the interval

(a) [/4, /2] (b) [–/4, 0]

(c) [, 5/4] (d) [3/4, ]

16. The value of cos [tan–1{sin(cot–1x)}] is

(a)1x

x2

2

(b)

1x

1x2

2

(c)2x

1x2

2

(d)

1x

2x2

2


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MT – 11

ANSWERS (INITIAL STEPEXERCISE)

1. d

2. b

3. b

4. a

5. c

6. a

7. a

8. b

9. a

10. a

11. c

12. d

13. b

14. a

15. a

16. c

ANSWERS (FINAL STEP EXERCISE)

1. c

2. c

3. b

4. a

5. d

6. d

7. b

8. b

9. c

10. c

11. d

12. d

13. b

14. b

15. b

16. b

10. If |2a sin2 + 2b sin cos + 2c cos2 – a – c | k areequality holds for some value of , then k2 =

(a) a2 + (b – c)2 (b) c2 + (a – b)2

(c) b2 + (a – c)2 (a) none of these

11. If 20 sin2 + 21 cos – 24 = 0 &

24

7 then

the values of cot 2

is :

(a) 3 (b)3

15

(c)3

15 (d) – 3

12. If + + + = , then sin2 + sin2 + sin2 +sin2 =

(a) cossinsin4

(b) sincossin4

(c) sinsincos4

(d) sinsinsin4

13. Two vertical poles 20 m and 80 m high stand aparton a horizontal plane. The height of the point ofintersection of the lines joining the top of each poleto the foot of the other is

(a) 15 m (b) 16 m

(c) 18 m (d) 50 m

14. A pole stands vertically, inside a triangular parkABC. If the angle of elevation of the top of the polefrom each corner of the park is same, then in ABC,the foot of the pole is at the

(a) centroid (b) circumcentre

(c) incentre (d) orthocentre

15. A vertical pole subtends an angle tan–1(1/2) at apoint P on the ground. The angle subtends by theupper half of the pole at the point P is

(a) tan–1(1/4) (b) tan–1(2/9)

(c) tan–1(1/8) (d) tan–1(2/3)

16. A pole of height h stands at one corner of a park inthe shape of an equilateral triangle. If is the anglewhich the pole subtends at the midpoint of theopposite side, the length of each side of the park is

(a) (3/2) h cot (b) (2/3) h cot

(c) (3/2) h tan (d) (2/3) h tan


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MT – 12

AIEEE ANALYSIS [2002]

1. In a triangle ABC, 2 ca 2

CBAsin

is equal to

(a) a2 + b2 – c2 (b) c2 – a2 – b2

(c) c2 + a2 – b–2 (d) b2 – c2 – a2

2.

9

2tan

4

1tan 11 equal to

(a)

5

3tan

2

1 1 (b)

2

1tan 1

(c)

5

3cos

2

1 1 (d)

5

3sin

2

1 1

3. The equation

a sin x + b cos x = c, where |c| > 22 ba has

(a) infinite no. of solutions

(b) no solutions

(c) a unique solution

(d) none of these

4. If tan = 3

4 then sin is

(a)5

4notbut

5

4

(b)5

4notbut

5

4

(c)5

4or

5

4

(d) none of these

5. In a ABC, 5

2

2

Ctan,

6

5

2

Atan then

(a) a, c, b are in A.P.

(b) a, b, c are in A.P.

(c) b, a, c are in A.P.

(d) a, b, c are in G.P.

6. cos sin ( – ) + cos sin ( – ) + cos sin( – ) =

(a) 0

(b) 4 cos cos cos

(c) 1

(d) 1/2

7. If is a root of 25cos2 + 5cos – 12 = 0

2 then sin 2 is equal to

(a)25

24(b)

18

13

(c)18

13(d)

25

24

8. The value of 15tan1

15tan12

2

is

(a) 1 (b) 2

(c) 3 (d)2

3

9. If sin ( + ) = 1, sin ( – ) = 2

1then

tan ( + 2) tan (2 + ) is equal to

(a) zero (b) –1


10. In a triangle ABC,

a = 4, b = 3, A = 600, then c is the root of theequation

(a) c2 – 3c + 7 = 0 (b) c2 – 3c – 7 = 0

(c) c2 + 3c – 7 = 0 (d) c2 + 3c + 7 = 0

11. xcostancoscot 11 then sin x =

(a)

2tan2 (b)

2cot

(c) tan (d)

2cot2

12.2

2

)yx(

xy4sin

is true if and only if

(a) x + y = 0 (b) x = y, x 0

(c) x 0, y 0 (d) x – y 0


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MT – 13


13. The trigonometric equation

sin–1x = 2sin–1a, has a solution for

(a) all real values of a

(b)2

1|a|

(c)2

1|a|

(d)2

1|a|

2

1

14. The upper 3/4 th portion of a vertical pole subtendsan angle tan–1(3/5) at a point in the horizontal planethrough its foot and at a distance 40 m from thefoot. A possible height of the vertical pole is

(a) 40 m (b) 60 m

(c) 80 m (d) 20 m

15. In a triangle ABC, medians AD and BE are drawn.

If AD = 4, DAB = 6

and ABE =

3

, then the

area of the ABC is

(a) 16/3 (b) 32/3

(c) 64/3 (d) 32/33

16. If in a triangle ABC

2

b3

2

Acosc

2

Ccosa 22

, then the sides a,

b and c

(a) are in G.P.

(b) are in H.P.

(c) satisfy a + b = c

(d) are in A.P.

17. The sum of the radii of inscribed and circumscribedcircles for an n sided regular polygon of side a, is

(a)

n2cot

2

a(b)

n2cota

(c)

n2cot

4

a(d)

ncota

AIEEE ANALYSIS [2004/2005]

18. Let , be such that < – < 3.If sin + sin = –21/65, and cos + cos = –27/65,

then the value of cos 2

is

(a)65

6(b)

130

3

(c)130

3 (d)

65

6

[2004]

19. The sides of a triangle are sin , cos and

cossin1 for some 0 < < 2

. The the

greatest angle of the triangle is

(a) 1200 (b) 900

(c) 600 (d) 1500

[2004]

20. A person standing on the bank of a river observesthat the angle of elevation of the top of the tree onthe opposite bank of the river is 600 and when theretires 40 meters away from the tree, the angle ofelevation becomes 300. The breadth of the river is

(a) 40 m (b) 30 m

(c) 20 m (d) 60 m

[2004]

21. In a triangle ABC, let C = 2

. If r is the inradius

and R is the circumradius of the triangle ABC, then2(r + R) equals

(a) a + b (b) b + c

(c) c + a (d) a + b + c

[2005]


New Delhi – 110 018, Ph. : 9312629035, 8527112111

MT – 14

22. If cos–1x – cos–1

2

y = , then 4x2 – 4xy cos + y2 is

equal to

(a) 4 (b) 2 sin 2

(c) –4sin2 (d) 4sin2

[2005]

23. If in a ABC, the altitudes from the vertices A, B,C on opposite sides are in H.P., then sin A, sin B,sin C are in

(a) A.P.

(b) G.P.

(c) H.P.

(d) Arithmetic-Geometric Progression

[2005]


24. If 0 < x < , and cos x + sin x = 2

1, then tan x is

(a) (1 + 7)/4 (b) (1 – 7)/4

(c) (4 – 7)/3 (d) –(4 + 7)/3


25 If 24

5eccos

5

xsin 11

then a value of x is

(a) 4 (b) 5

(c) 1 (d) 3

26. A tower stands at the centre of a circular park. Aand B are two points on the boundary of the parksuch that AB (=a) subtends an angle of 600 at thefoot of the tower, and the angle of elevation of thetop of the tower from A or B is 300. The height ofthe tower is

(a) a/3 (b) a3

(c) 2a/3 (d) 2a3

ANSWERS AIEEE ANALYSIS

1. c 2. b 3. b 4. c 5. b 6. b 7. d

8. d 9. c 10. a 11. a 12. b 13. d 14. a

15. d 16. d 17. a 18. c 19. a 20. c 21. a

22. d 23. a 24. d 25. d 26. a


New Delhi – 110 018, Ph. : 9312629035, 8527112111

MT – 15

TEST YOURSELF

1. If A and B be acute positive angles satisfying

3sin2A + 2sin2B = 1, 3 sin 2A – 2 sin 2B = 0

then

(a) B = /4 – A/2 (b) A = /4 – 2B

(c) B = /2 – A/4 (d) A = /4 – B/2

2. If 5

ztan

3

ytan

2

xtan and x + y + z = , then the

value of tan2x + tan2y + tan2z is

(a) 38/3 (b) 38

(c) 114 (d) 19

3. If tan A – tan B = x and cot B – cot A = y, then thevalue of cot (A – B) is

(a)xy

yx (b) 22 y

1

x

1

(c)xy

yx (d) xy

4. The value of cos–1 (cos (–17/5), is equal to

(a) –17/5 (b) 3/5

(c) 2/5 (d) none of these

5. The value of sin (cot–1(cos(tan–1x))) is

(a)1x

2x2

2

(b)

2x

1x2

2

(c)2x

x

2 (d)

2x

1

2

6.ca

)cba(btan

bc

)cba(atan 11

ab

)cba(ctan 1

is equal to

(a) /4 (b) /2

(c) (d) 0

ANSWERS

1. a

2. a

3. c

4. b

5. b

6. d

trigonometryeinsteinclasses.com/trigonometry(s).pdf[answers : (1) d (2) a (3) a (4) b (5) d (6) a]...

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