Question

dx39. equalssin2x cosx(A) tan x+ cot x C(B) tan x - cot x + C(D) tan x - cot 2x + C(C) tan x cotxC

Answer 1

Let the integral be I,

I= ∫ 1 sin 2 x cos 2 x dx

Simplify the above integral.

I= ∫ sin 2 x+ cos 2 x sin 2 x cos 2 x dx = ∫ sin 2 x sin 2 x cos 2 x dx + ∫ cos 2 x sin 2 x cos 2 x dx = ∫ sec 2 xdx + ∫ cos ec 2 xdx =tanx−cotx+C

Hence, the correct option is (B).