Question

Solve the following equation:
$(1-\tan x)(1+\sin 2x)=1+\tan x$

Answer 1

$(1-\tan x)(1+\sin 2x)=1+\tan x$

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

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

$\sin x+\cos x=0$ or ${\cos }^{2}x-{\sin }^{2}x=1$

$\tan x=-1$ or $\cos 2x=0$

$x=n\pi +\frac{3\pi }{4}$ or $x=\frac{(2m+1)\pi }{4}$