Question

Solve the following system.
${}_{tanx-tany=2.}^{x+y\frac{3\pi }{4},}$

Answer 1

$x+y=\frac{3\pi }{4}$

$\Rightarrow \tan x-\tan y$

$\Rightarrow \frac{\sin x}{\cos x}-\frac{\sin y}{\cos y}$

$\frac{\sin \left(3\pi /4\right)}{\cos x\cos y}=2;\cos x\cos y=\frac{\sqrt{2}}{4}$

$\Rightarrow \cos x\cos y=\frac{1}{2\sqrt{2}}$