Prove the identity

Question

csc^2x = 2sec2x / sec2x - 1

Sorry i really tried. I got : LS = 1 - (cos^2x/sin^2x) but that's it. please help

Answer 1

multiply RS top and bottom by cos2x and you have

2/(1-cos2x)
= 2/(1-(cos^2 x - sin^2 x))
= 2/(1-cos^2 x + sin^2x)
= 2/(2sin^2 x)
= 1/sin^2 x
= csc^2 x