Question

Solve the following equation:
$\sin x-\cos x=1$

Answer 1

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

$\sin (x-\frac{\pi }{4})=\frac{1}{\sqrt{2}}$

$x-\frac{\pi }{4}=n\pi +{(-1)}^n\frac{\pi }{4}$

$x=n\pi +{(-1)}^n\frac{\pi }{4}+\frac{\pi }{4}.$