Prove these identites

Question

I really need help with these I don't understand how to do them !!!!

sin^2+tan^2=sec^2-cos^2

sin^2 sec^2 +sin^2=tan^2+sin^2

Answer 1

a good place to start is usually to make everything sin/cos:

sin^2 + sin^2/cos^2
[(1-cos^2)cos^2 + sin^2]/cos^2
(cos^2 - cos^4 + 1 - cos^2)/cos^2
(1 - cos^4)/cos^2
1/cos^2 - cos^2
sec^2 - cos^2
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sin^2/cos^2 + sin^2
tan^2 + sin^2