Simplify the fraction [cosx*sin(2x)-2sinx]/sin^2 x*cosx=?

We have to simplify: [cos x*sin(2x) - 2 sin x]/(sin x)^2
*cos x

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

use sin 2x = 2*sin x * cos
x

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

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

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

=> [2*cos x/ sin x] - [4/ 2*sin x*cos
x]

=> [2*cos x/ sin x] - [4/ sin
2x]

=> 2*cot x - 4*cosec
2x

The required result is 2*cot x - 4*cosec
2x