Question

Solve the following equations.
$sinx+cosx=\sqrt{2}sin5x.$

Answer 1

$\frac{\sin x}{\sqrt{2}}+\frac{\cos x}{\sqrt{2}}=\sin 5x$

$\cos (x-\frac{\pi }{4})=\cos (2n\pi +\frac{\pi }{2}-5x)$

$\cos (x-\frac{\pi }{4})=\cos (2n\pi +\frac{\pi }{2}-5x)$

$x=n\frac{\pi }{3}+\frac{\pi }{8}.$