1. verify the following trigonometric identities and show all steps

let @=theta

1. cos^3@+sin^2@cos@=cos

2. cot@

---- = tan@

csc^2@-1

3. cot@csc@tan^2@=sec@

4. sin@ (1 + csc@)=sin@+1

5. cos@=sec@ - sin@tan@

6. 1+cos@ = cot@(sin@+tan@)

Answering any part of these would help a ton! Thanks.