Question

verify that (cscx-cotx)^2 = 1-cosx/1+cosx

Answer 1

\[\begin{align*}(\csc x-\cot x)^2&=\frac{1-\cos x}{1+\cos x}\\
&=\frac{1-\cos x}{1+\cos x}\cdot\frac{1-\cos x}{1-\cos x}\\
&=\frac{(1-\cos x)^2}{(1-\cos^2 x}\end{align*}\]
What can you do with this?

Answer 2

can you multiply by the conjugate

Answer 3

Yeah, that's what I did. (1 - cosx) is the conjugate of (1 + cosx).