Question

Solve the equation.cos x = 1

Answer 1

cos x = 1
cos x= cos 0°
x = 0°

Answer 2

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.

we know that cos 0° = 1

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

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

Thus

$x = 0$