Question

Verify the identity:
sin²x - sin x/1- cos²x = sin x - 1/sin x

Answer 1

See below for proof

Explanation:

`\displaystyle (\sin^2x-\sin x)/(1-\cos^2x)\\\\=(\sin^2x-\sin x)/(\sin^2x)\\\\=(\sin x-1)/(\sin x)`

Thus, the identity is proven. Note that
`\cos^2x+\sin^2x=1` by the Pythagorean Identity and canceling out
`\sin x` in the second step gets us our correct answer.