Find the value of the following: 1. 1 13 cos cos 6 p 2. 1 7 tan tan 6 p Prove that 3. 1 3 1 24 2sin tan 5 7 = 4. 1 8 1 3 1 77 sin sin tan 17 5 36 + = 5. 1 4 1 12 1 33 cos cos cos 5 13 65 + = 6. 1 12 1 3 1 56 cos sin sin 13 5 65 + = 7. 1 63 1 5 1 3 tan sin cos 16 13 5 = + 8. 1 1 1 1 1 1 1 1 tan tan tan tan 5 7 3 8 4 p Prove that 9. 1 1 1 1 tan cos 2 1 x x x = + , x [0, 1] 10. 1 1 sin 1 sin cot 1 sin 1 sin 2 x x x x x + + = + , 0, 4 x p 11. 1 1 1 1 1 tan cos 1 1 4 2 x x x x x + p = + + , 1 1 2 x [Hint: Put x = cos 2q] 12. 9 9 1 1 9 1 2 2 sin sin 8 4 3 4 3 p = Solve the following e
Find the value of the following:
Question 1: β1 13 cos cos 6 Ο
Question 2: β1 7 tan tan 6 Ο Prove that
Question 3: β1 3 β1 24 2sin tan 5 7 =
Question 4: β1 8 β1 3 β1 77 sin sin tan 17 5 36 + =
Question 5: β1 4 β1 12 β1 33 cos cos cos 5 13 65 + =
Question 6: β1 12 β1 3 β1 56 cos sin sin 13 5 65 + =
Question 7: β1 63 β1 5 β1 3 tan sin cos 16 13 5 = +
Question 8: β1 1 1 1 1 1 1 1 tan tan tan tan 5 7 3 8 4 β β β p Prove that
Question 9: β1 1 β1 1 tan cos 2 1 x x x β = + , x Γ [0, 1]
Question 10:β1 1 sin 1 sin cot 1 sin 1 sin 2 x x x x x + + β = + β β , 0, 4 x Ο Γ
Question 11:β1 1 1 1 β1 tan cos 1 1 4 2 x x x x x + β β p = β + + β , 1 1 2 β β€ x β€ [Hint: Put x = cos 2q]
Question 12:9 9 1 1 9 1 2 2 sin sin 8 4 3 4 3 Ο β β β = Solve the following equations:
Question 13:2tanβ1 (cos x) = tanβ1 (2 cosec x)
Question 14: β1 1 1 β1 tan tan ,( 0) 1 2 x x x x β = > +
Question 15:sin (tanβ1 x), | x| < 1 is equal to (A) 2 1 x β x (B) 2 1 1β x (C) 2 1 1+ x (D) 2 1 x + x
Question 16:sinβ1 (1 β x) β 2 sinβ1 x = 2 p , then x is equal to (A) 0, 1 2 (B) 1, 1 2 (C) 0 (D) 1 2
Question 17: 1 1 tan tan x x y y x y β β β β + is equal to (A) 2 p (B) 3 p (C) 4 p (D) 3 4 β p
