Question

Solve the equation.
cos 3x = $\frac{1}{\sqrt{2}}$

Answer 1

As we know that principal value branch of cos inverse is [0,π]

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

$cos\: 3x = \frac{1}{\sqrt{2}}\\ \\ 3x = {cos}^{-1}{ \frac{1}{\sqrt{2}}} \\ \\ 3x = {cos}^{ - 1} (cos (π/4))$

here both cancels with each other because π/4 belongs to [0,π]

Thus

$3x = π/4\\\\x=π/12$