Question

Solve the following equations.
$\sin 5x\sin 3x=0$.

Answer 1

$\sin \left(5x\right)\sin \left(3x\right)=0$

Solving each part separately :

$\sin 5x=0$ or $\sin \left(3x\right)=0$

if $\sin 5x=0$

$\Rightarrow 5x=0+2\pi n$ or $5x=\pi +2\pi n$

$x=\frac{2}{5}\pi n$ or $x=\frac{\pi +2\pi n}{5}$

Similarly,

if $\sin 3x=0$

$\Rightarrow 3x=0+2\pi n$ or $3x=\pi +2\pi n$

$x=\frac{2}{3}\pi n$ or $x=\frac{\pi +2\pi n}{3}$

Combine all the solutions:-

$x=\frac{2\pi n}{5},x=\frac{\pi }{5}+\frac{2\pi n}{5},x=\frac{2\pi n}{3},x=\frac{\pi }{3}+\frac{2}{3}\pi n$.