I don't understand,please be clear!

Prove that each equation is an identity.
I tried to do the problems, but I am stuck.

1. cos^4 t-sin^4 t=1-2sin^2 t

2. 1/cos s= csc^2 s - csc s cot s

3. (cos x/ sec x -1)- (cos x/ tan^2x)=cot^2 x

4. sin^3 z cos^2 z= sin^3 z - sin^5 z

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