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

User Pupper
by
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1 Answer

5 votes

Answer:

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.

User Asif Karim Bherani
by
7.9k points