Verifying Identities

[lewch45]

Can someone please help with this one.

1 + sin x = cos^2 x/ 1 - sin x

Any help would be appreciated. Thanks.

 

[soroban]

Hello, lewch45!

\(\displaystyle 1\,+\,\sin x \:= \:\L\frac{\cos^2x}{1\,-\,\sin x}\)

The right side is: \(\displaystyle \L\,\frac{1\,-\,\sin^2x}{1\,-\,\sin x}\;=\;\frac{(\sout{1\,-\,\sin x})(1\,+\,\sin x)}{\sout{1\,-\,\sin x}}\)\(\displaystyle \;=\;1\,+\,\sin x\)