Question

Total number of solution(s) of the equation $\sin 4x+\cos 4x=2$ in $[-2\pi ,2\pi ]$ is :

Answer 1

$\sin 4x+\cos 4x=2$
$\because \sin 4x\le 1$ and $\cos 4x\le 1$
So, it is possible only, when
$\sin 4x=1$ and $\cos 4x=1$
Which is not possible as ${\sin }^2\theta +{\cos }^2\theta =1$
$\Rightarrow$ Hence, there is no solution.