Question

Solve the equation.
cos $\frac{5x}{2}$ = 0

Answer 1

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/2= 0

$cos \frac{5x}{2}= 0\\ \\ \frac{5x}{2}= {cos}^{-1}(0) \\ \\ \frac{5x}{2} = {cos}^{ - 1} (cos (\frac{\pi}{2}))$

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

Thus

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