How do you simplify sin^2x csc^2x - sin^2x?

1 Answer
Sep 3, 2015

The expression simplifies into cos^2(x)

Explanation:

You only need to write down the definitions: since csc(x)=1/{\sin(x)}, we have that

\sin^2(x) * csc^2(x) - \sin^2(x) = {\sin^2(x)}/{\sin^2(x)} - \sin^2(x)

The first term is obviously 1, so you have 1-\sin^2(x), which equals \cos^2(x) because of the fundamental formula \cos^2(x)+\sin^2(x)=1