Mahaveer Classes , Chaitanya Nagar, Ganesh Colony, Jalgaon (MH) Phone - 0257-2254545 PRACTICE WORK JEE (Mains) SUB : MATH TRIGONOMETRIC RATIOS & IDENTITIES 1. If α is a root of 25 0 12 cos 5 cos 2 = - θ + θ , , 2 / π < α < π then sin 2α is equal to [AIEEE-2002] (a) 25 / 24 (b) 25 / 24 - (c) 18 / 13 (d) 18 / 13 - 2. If , 0 , ec cos sin y 2 2 ≠ θ θ + θ = then [AIEEE-2002] (a) 0 y = (b) 2 y ≤ (c) 2 y - ≥ (d) 2 y > 3. If sin( ) 1, sin ( ) 1 / 2, α β α β + = - = then ) 2 ( tan ) 2 tan( β + α β + α is equal to [AIEEE-2002] (a) 1 (b) -1 (c) zero (d) None 4. If , 3 / 4 tan - = θ then sin θ is (a) 5 / 4 not but 5 / 4 - (b) 4/5 4/5 or - (c) 5 / 4 not but 5 / 4 - (d) None of these 5. The value of 0 2 0 2 15 tan 1 15 tan 1 + - is [AIEEE-2002] (a) 1 (b) 3 (c) 2 / 3 (d) 2 6. 2 2 ) y x ( xy 4 sin + = θ is true, if and only if [AIEEE-2002] (a) 0 y x ≠ - (b) y x - = (c) y x = (d) 0 y , 0 x ≠ ≠ 7. In a ABC Δ , 2 sin 2 A B C ac - + = [IIT-2000],[AIEEE-2002] (a) 2 2 2 c b a - + (b) 2 2 2 b a c - + (c) 2 2 2 a c b - - (d) 2 2 2 b a c - - 8. In a ΔABC, tan A/2 = 5/6, tan C/2 = 2/5, then [AIEEE-2002] (a) a, c, b are in AP (b) a, b, c are in AP (c) b, a, c are in AP (d) a, b, c are in GP 9. In a triangle ABC, a = 4, b = 3, ∠ A = 60 0 , then c is the root of the equation [AIEEE-2002] (a) 0 7 c 3 c 2 = - - (b) 0 7 c 3 c 2 = + + (c) 0 7 c 3 c 2 = + - (d) 0 7 c 3 c 2 = - + 10. If in a triangle ABC , 2 / b 3 ) 2 / A ( cos c ) 2 / C ( cos a 2 2 = + then the sides a, b,c are in [AIEEE-2003] (a)AP (b)GP (c)HP (d)satisfy a + b = c 11. The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is [AIEEE-2003] (a) a cot (π/n) (b) a/2 cot (π/2n) (c) a cot (π/2n) (d) a/4 cot (π/2n) 12. If in a ΔABC, the altitudes from the vertices A, B, C on opposite sides are in HP, then sin A, sin B, sin C are in [AIEEE-2003] (a) HP (b) AGP (c) AP (d) GP 13. The sides of a triangle are sin α, cos α and α α + cos sin 1 for some 0 < α < π/2). Then the greatest angle of the triangle is [AIEEE-2004] (a) 60 0 (b) 90 0 (c) 120 0 (d) 150 0 14. Let β α, be such that . 3π < β - α < π If , 65 / 27 cos cos and 65 / 21 sin sin - = β + α = β + α then the value of cos β - α 2 is [AIEEE-2004] (a) 130 / 3 - (b) 130 / 3 (c) 65 / 6 (d) 65 / 6 - 15. In a triangle ABC, let 2 C π ∠ = .If r is the inradius and R is the circumradius of the triangle ABC,then 2(r+R) equals [AIEEE-2005] (a) b+c (b) a+b (c) a+b+c (d) c+a 16. Let A and B denote the statements : cos cos cos 0 A α β γ + + = : sin sin sin 0 B α β γ + + = If ( ) ( ) ( ) 3 cos cos cos 2 α β β γ γ α - + - + - =- then [AIEEE-2009] (a) A is true and B is false (b) A is false and B is true (c) both A and B are true (d) both A and B are false 17. Let ( ) 4 cos 5 α β + = and let ( ) 5 sin 13 α β - = , where 0 , 4 π αβ ≤ ≤ , then tan 2 α = [AIEEE-2010] (a) 56 33 (b) 19 12 (c) 20 7 (d) 25 16 18. For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is , there is a regular polygon with r R = [AIEEE-2010] (a) 1 2 (b) 3 2 (c) 2 3 (d) 1 2 19. The expression tan cot 1 cot 1 tan A A A A + - - can be written as [JEE MAINS-2013] (a) sin A cos A + 1 (b) secA cosec A + 1 (c) tan A + cot A (d) sec A + cosec A
