Question

Evaluate : $\cos 5x+\cos 3x=0$

Answer 1

$cos5x+cos3x=0$

$\Rightarrow 2cos\left[\frac{5x+3x}{2}\right]cos\left[\frac{5x-3x}{2}\right]=0$

$\Rightarrow 2cos4xcosx=0$

$\Rightarrow cosx=0$ or $cos4x=0$

$\Rightarrow x\in \frac{n\pi }{2}$ or $4x\in \frac{n\pi }{2}n\in N$

$\Rightarrow x\in \frac{n\pi }{8}n\in N$

Solution set of cos $5x+cos3x=0$ is

$x=\frac{n\pi }{8}$