Question

How do you simplify `(sinxcosx)/(1-sin^2x)`?

Answer 1

The answer is `\tan(x)`

Explanation:

By the fundamental formula `sin^2(x)+cos^2(x)=1`, you have that `1-\sin^2(x)=\cos^2(x)`. So, your fraction becomes

`{\sin(x)\cos(x)}/{\cos^2(x)}`, and you can simplify a cosine to obtain `\sin(x)/\cos(x)`, which is exactly `\tan(x)`.