Question

$\frac{\cos A\csc A-\sin A\sec A}{\cos A+\sin A}-\csc A+\sec A.$

Answer 1

$\frac{\cos A\csc A-\sin A\sec A}{\cos A+\sin A}-cscA+\sec A$

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

$=\frac{{\cos }^{2}A-{\sin }^{2}A}{\left(\sec A\cos A\right)(\cos A+\sin A)}-\csc A+\sec A$

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

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

$=0$