Prove that $\frac{\cot A-\cos A}{\cot A+\cos A}=\frac{\cos ecA-1}{\cos ecA+1}$

$\frac{\cot A-\cos A}{\cot A+\cos A}$

  $\frac{\frac{\cos A}{\sin A}-\cos A}{\frac{\cos A}{\sin A}+\cos A}=\frac{\cos A-\cos A\sin A}{\cos A+\cos A\sin A}$

                             $=\frac{\cos A\left(1-\sin A\right)}{}\cos A\left(1+\sin A\right)$

                        $=\frac{\frac{1}{\sin A}-\frac{\sin A}{\cos A}}{\frac{1}{\sin A}+\frac{\sin A}{\sin A}}$   

                             $=\frac{\cos ecA-1}{\cos ecA+1}$