How do i solve the double angle identity proof 2csc^2x = sec^2xcotx

Question

In this problem I need to prove that both identies are equal to eachother

Answer 1

Given 2Csc^2x = Sec^2xCotx

I assume it 2Csc2x = Sec^2xCotx

Right hand side identity = Sec^2xCotx

= (1/cos^2x)(Cosx/Sinx)

= (1/CosxSinx)

Multiple with 2 to numarator and denominator.

= 2/2CosxSinx

= 2/2SinxCosx

= 2/Sin2x

= 2*1/Sin2x

= 2Csc2x

= Left hand side identity.