Question

Prove this to be true. Cscx-Sinx=Cosx(Cotx)

Answer 1

\[\csc(x) - \sin(x) = \cos(x) \dot\ \cot(x)\]\[\frac{1}{\sin(x)}-\frac{\sin^2(x)}{\sin(x)} = \frac{\cos^2(x)}{\sin(x)}\]\[\frac{1-\sin^2(x)}{\sin(x)}=\frac{\cos^2(x)}{\sin(x)}\]

Because \[1-\sin^2(x)=\cos^2(x)\] then, \[\frac{\cos^2(x)}{\sin(x)}=\frac{\cos^2(x)}{\sin(x)}\]

Therefore: \[\csc(x) - \sin(x) = \cos(x) \dot\ \tan(x)\] is true.

Answer 2

nice:)

Answer 3

I know some people like it when you make the left side equal the right side, but this is also a valid approach