Question

Solve the equation.sec x = √2

Answer 1

As we know that principal value branch of sec inverse is [0,π]-{ π/2}

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

$sec x= \sqrt{2}\\ \\ x= {sec}^{-1}(\sqrt{2}) \\ \\ x = {sec}^{ - 1} (sec (π/4))$

here both cancels with each other because π/4 belongs to [0,π]-{ π/2}

Thus

$x = π/4$