Exercise miscellaneous

-1 1 sin 1 sincot 21 sin 1 sin

x x   + + − =  + − −  , 0, 4x π ∈  

-1 -11 1 1tan cos4 21 1

x x   + − − π = −   + + −  , 1 1 x− ≤ ≤ [Hint: Put x = cos 2θ] Solve the following equations:

2tan-1 (cos x ) = tan -1 (2 cosec x) 12. -1 -11 1tan tan ,( 0)1 2 x x xx − = >+

sin (tan-1 x), | x | < 1 is equal to

(A) 21 / x / x− (B) 2 / 1 x− (C) 2 / 1 x+ (D) 21 / x / x+

sin-1 (1 - x) - 2 sin-1 x = 2 π , then x is equal to (A) 0, 1 / 2 (B) 1, 1 2 (C) 0 (D) 1