There's some ambiguity in the way you typed the right side of the equation, but the left reduces down to this:
I have
1/sin^2(t) + 1/cos^2(t) = 1/sin^2(t)-sin^4(t)
I started on the right side of the identity and got to this stage:
1/sin^2(t) + 1/1-sin^2(t)
On the left side of the identity I got to this stage:
1/sin^2(t)(1-sin^2(t))
I know I need to go farther on the right side of the identity but I am stuck at this point. Any help would be great thanks!