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