Take home stuff due tomorrow...the applied trig I understand...heights of mountains and such, but the theory is lost on me. The following are all questions from the assignment to which I do not know the answers. Any help would be appreciated. Thank you in advance.

Prove the identity.

1) ([5(csc^2)x] + 4cscx - 1)/[(cot^2)x] = [5cscx-1]/[cscx-1]

2) cosx/secx-1 - cosx/secx+1 = 2cosx/tan^2x

3) csc^4 - cot^4x = csc^2x + cot^2x

4) cos[x+[y-(pi/2)]] = sin(x+y)