We have y = cos 2x / (cos x)^2*(sin x)^2

y = cos 2x / (cos x)^2*(sin x)^2

=> [(cos x)^2 - (sin x)^2] / (cos x)^2*(sin x)^2

=> 1/ (sin x)^2 - 1/ (cos x)^2

Now the integral of 1/ (sin x)^2 = -1 / tan x and the intgral of 1/ (cos x)^2 is tan x

Therefore Int [1/ (sin x)^2 - 1/ (cos x)^2]

=> -cot x - tanx + C

**So the required integral is -cot x - tanx + C **