Question

Find the principal solution of the equation.
cos x = 1/2

Answer 1

Q. cos x = 1/2
S. cox x = cos 60
so,
x=60

Answer 2

Solution:
➖➖➖

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 π/3= 1/2

$cos x= \frac{1}{2}\\ \\ x= {cos}^{-1}(\frac{1}{2}) \\ \\ x = {cos}^{ - 1} (cos (\frac{\pi}{3}))$

here both cancels with each other because π/3 belongs to [0,π]

Thus

$x= (\frac{\pi}{3})$