SOLUTION: Prove the identity: Tan^2(x)/(1+tan^2(x)) = sin^2(x)

Question 889493: Prove the identity:
Tan^2(x)/(1+tan^2(x)) = sin^2(x)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

you will use the identiTy tan^2(x) + 1 = sec^2(x)

your equation becomes:

tan^2(x) / sec^(x) = sin^2(x)

since sec^(x) = 1/cos^2(x), your equation becomes:

tan^2(x) * cos^2(x) = sin^2(x)

since tan^2(x) = sin^2(x) / cos^2(x), your equation becomes:

sin^2(x) / cos^2(x) * cos^2(x) = sin^2(x)

the cos^2(x) in the numerator and denominator cancel out and you are left with:

sin^2(x) = sin^2(x)

QED (means proof is done)

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