Question

Verify the identity.

(cot x)/1+csc x)=(csc x-1)/(cot x)

need help please!!!! Showing work will help a lot

Answer 1

`(\cot x)/(1+\csc x)=(\csc x-1)/(\cot x)\\ \cot^2 x=(1+\csc x)(\csc x-1)\\ \cot^2 x=-(1+\csc x)(1-\csc x)\\ \cot^2 x=-(1-\csc^2 x)\\ \cot^2 x=-1+\csc^2 x\\ \left((\cos x)/(\sin x)\right)^2=-1+\left((1)/(\sin x)\right)^2\\ (\cos^2 x)/(\sin ^2x)=-1+(1)/(\sin^2 x)\\ \cos^2 x=-\sin^2x +1\\ \boxed{\sin^2 x+\cos ^2 x=1}`