Question

Solve for x and y :
$x+y=\frac{7\pi }{4},\frac{\sin x}{\cos y}=-\sqrt{2}$

Answer 1

Solution-

$x+y=\frac{7\pi }{4},\frac{sinx}{cosy}=-\sqrt{2}$

$sinx=-\sqrt{2}cos(\frac{7\pi }{4}-x)$

$sinx=-\sqrt{2}cos(\frac{3\pi }{2}+\frac{\pi }{4}-x)$

$sinx=-\sqrt{2}sin(\frac{\pi }{4}-x)$

$x=\frac{\pi }{2}$ $y=\frac{7\pi }{4}-\frac{\pi }{2}=\frac{5\pi }{4}$