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Proving Trigonometric Identities (5 Problems)

Prove the following identities..."not an identity" is an option.
Please explain in detail and in steps how to perform the following:

1. cot²x-cos²x=cos²xcot²x

3. tanx= square rt of sec²x-1

4. sinx/1-cotx + cosx/1-tanx=cosx+sinx

5. cotx-1/1-tanx = cscx/secx

6. cosxsiny=1/2(sin(x+y)-sin(x-y)

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Solution Summary

Trigonometric identities are proven. The solution is detailed and well presented.