Question

Solve the following system.
${}_{cosxcosy=\frac{1}{2}.}^{tanx+tany=2,}$

Answer 1

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

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

$\Rightarrow \frac{\sin (x+y)}{1/2}=2$

$\Rightarrow \sin (x+y)=1$

$x+y=\frac{(2n+1)\pi }{2}$