could see some examples of trigonometry with their solutions:Solved ExamplesQuestion1:Prove the following identity:

Solution:LHS =(sec- cose)(1 + tan+ cot)=(sincossincos)(sincos+1sincos)[Using identities, sec=1cos, cose=1sin, tan=sincosand cot=cossin]=(sincos)(sincos+1)sin2cos2=(sincos)(sincos+sin2+cos2)sin2cos2[Using,sin2+cos2= 1]

= tansec- cotcosc= RHS

Question2:Prove the following identity:

Solution:LHS = 1 + 2sec2A tan2A - sec4A - tan4A

= 1 - (sec4A - 2sec2A tan2A + tan4A)

[Using identity, sec2A - tan2A = 1]

= 1 - 1

= 0

= RHSQuestion3:Prove the following identity:

Solution:LHS =[1sinAcosAcosA(secAcosecA)][sin2Acos2Asin3A+cos3A]

= [1sinAcosAcosA(1cosA1sinA)][(sinA+cosA)(sinAcosA)(sinA+cosA)(sin2AsinAcosA+cos2A)]

[Using identities, sec=1cos, cose=1sin, sin2A - cos2A = (sin A + cos A)(sin A - cos A) and sin3A + cos3A = (sin A + cos A)(sin2A - sin A cos A + cos2A)]

=[1sinAcosAsinAcosAsinA][sinAcosAsin2AsinAcosA+cos2A][By cancelling common terms]

= sin A[1sinAcosAsinAcosA] * [sinAcosA1sinAcosA]

[Using identity sin2A + cos2A = 1]

= sin A (By cancelling common terms)

= RHSTrigonometry Test QuestionsBack to Top

Lets us solve some more trigonometric examples using their identities:Solved ExamplesQuestion1:Prove the following identity:

Solution:LHS = (sec- 1)2- (tan- sin)2

= (1cos- 1)2- (sincos- sin)2

= (1coscos)2-sin2cos2(1 - sin*cossin)2

= (1coscos)2- (1 - cos)2sin2cos2

= (1 - cos)2[1cos2sin2cos2]

Question2:Prove the following identity:

Solution:LHS =tan31+tan2+cot31+cot2

=tan3sec2+cot3cose2

Trigonometry Sample QuestionsBack to Top

Solved ExamplesQuestion1:

Solution:If tan A + sin A = m .................. (1)tan A - sin A = n ................... (2)Step 1:Adding (1) and (2)

Step 2:Subtracting (2) from (1)

Now

[Using, (a + b)2= a2+ b2+ 2ab and (a - b)2= a2+ b2- 2ab]

Question2:Solution:

=12+1*2121cos

= (2- 1)cos

Question3:If x sin3+ y cos3= sincosand x sin- y cos= 0. Prove that x2+ y2= 1.

Solution:x sin3+ y cos3= sincos..................... (i)

x sin- y cos= 0 ...................... (ii)

from (i) and (iii)

y = sin.................. (iv)

From (iii) and (iv), x = cos

=> x2+ y2= sin2+ cos2

Question4:Solution:

[using identity1 - cos 2A = 2sin2Asimilarly, 1 - cos 8A = 2sin24A and 1 - cos 4A = 2sin22A ]

[Using identity,sin2A = 2sin A cos A]

Question5:Solution:Step 1:

[Using identity,cos 3A = 4cos3A - 3cosA]

[Using, cos2A =1+cos2A2]

or

Step 2:let A = 15