Question

Prove the Identityan%7D%5E%7B2%7D%20x%7Bsin%7D%5E%7B2%7D%20x" id="TexFormula1" title=" {tan}^{2} x - {sin}^{2} x = {tan}^{2} x{sin}^{2} x" alt=" {tan}^{2} x - {sin}^{2} x = {tan}^{2} x{sin}^{2} x" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

see below

Step-by-step 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

Answer 2

Answer:

check pic

step-by-step explanation

check pic