Prove the Identity {tan}^(2) x - {sin}^(2) x = {tan}^(2) x{sin}^(2) x ​

Question

Prove the Identity

`{tan}^(2) x - {sin}^(2) x = {tan}^(2) x{sin}^(2) x`
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Answer 1

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step-by-step explanation

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Answer 2

see below

Explanation:

tan ^2 x -sin ^2 x = tan ^2x sin ^2x

tan = sin / cos

sin ^2 x / cos ^2 x -sin ^2 x = sin ^2 x / cos ^2 x * sin^2 x

Multiply each side by cos ^2

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

sin ^2 x - cos ^2 x sin ^2 x = sin ^2 x * sin ^2x

Factor out sin ^2 x

sin ^2 x(1 - cos ^2 x) = sin ^2 x * sin^2 x

We know that 1 - cos ^2 x = sin ^2 x

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