Question

Solve$\int \frac{\cos 2x}{\cos x-\sin x}dx$

Answer 1

Now

$\int \frac{\cos 2x}{\cos x-\sin x}dx$

$=\int \frac{({\cos }^{2}x-{\sin }^{2}x)}{\cos x-\sin x}dx$

$=\int (\cos x+\sin x)dx$

$=\sin x-\cos x+c$ [$c$ being integrating constant]