Question

proove:

$\frac{cossAcosecA-sinAsecA}{cosA+sinA}$ = cosec A - sec

Answer 1

As $cosecA=\frac{1}{\sin A}$ & $\sec A=\frac{1}{\cos A}$

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

$=\frac{{\cos }^{2}A-{\sin }^{2}A}{\sin A\cos A(\sin A+\cos A)}$

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

$=\frac{1}{\sin A}-\frac{1}{\cos A}=cosecA-\sec A$.