Question

Solve the equation.
sin 3x = 0

Answer 1

As we know that principal value branch of sin inverse is [-π/2,π/2]

thus while solving the equation we must remember that sin inverse cancel sin x only if x belongs to principal value branch.

we know that sin 0° = 0

$sin\:3x= 0\\ \\ 3x= {sin}^{-1}(0) \\ \\ 3x = {sin}^{ - 1} (sin (0))$

here both cancels with each other because 0 belongs to [-π/2,π/2]

Thus

$3x = 0\\\\ x = 0$