Question

Prove : 1+cosA-sin2A/sinA*(1+cosA)= cotA

Answer 1

`(1+\cos A-\sin^2A)/(\sin A(1+\cos A))=\cot A\\\\L_s=((1-\sin^2A)+\cos A)/(\sin A(1+\cos A))=(\cos^2A+\cos A)/(\sin A(1+\cos A))\\\\=(\cos A(1+\cos A))/(\sin A(1+\cos A))=(\cos A)/(\sin A)=\cot A=R_s\\\\\text{Used:}\\\\\sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\\cot x=(\cos x)/(\sin x)`