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

The identity is false; it should read: 2cosec2x=sec^2xcotx. (Put x=30 degrees and you'll find that the original equation doesn't balance: 4=4/3*sqrt(3).)

This is the same as 2/sin2x=cosx/(cos^2xsinx)=1/(cosxsinx).

2/sin2x=2/(2sinxcosx)=1/(sinxcosx), so the two expressions are identical.