Question

Solve the equation.
cos (x + $\frac{\pi }{10}$) = 0

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.

we know that cos (π/2) = 0

$cos( x+\frac{\pi }{10})= 0\\ \\ ( x+\frac{\pi }{10})= {cos}^{-1}(0) \\ \\ ( x+\frac{\pi }{10}) = {cos}^{ - 1} (cos (\frac{\pi}{2}))$

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

Thus

$( x+\frac{\pi }{10}) = (\frac{\pi}{2})\\\\x = (\frac{\pi}{2})-\frac{\pi }{10}\\\\x=\frac{2\pi }{5}$