Question

Find $\frac{dy}{dx}$ when $y=\frac{1+\sin 2x-\cos 2x}{1+\sin 2x+\cos 2x}$.

Answer 1

$y=\frac{1+\sin 2x-\cos 2x}{1+\sin 2x+\cos 2x}$

$y=\frac{1+2\sin x\cos x-1+2{\sin }^{2}x}{1+2\sin x\cos x+2{\cos }^{2}x-1}$

$y=\frac{2\sin x(\cos x+\sin x)}{2\cos x(\sin x+\cos x)}$

$y=\tan x$

$dy/dx={\sec }^{2}x$