Question

Solve the equation.tan $\frac{2x}{3}$ = √3

Answer 1

As we know that principal value branch of tan inverse is [-π/2,π/2]

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

$tan\frac{2x}{3} = \sqrt{3}\\ \\ \frac{2x}{3} = {tan}^{-1}(\sqrt{3}) \\ \\ \frac{2x}{3} = {tan}^{ - 1} (tan (π/3))$

here both cancels with each other because π/3 belongs to [-π/2,π/2]

Thus

$\frac{2x}{3} = π/3\\\\2x=π \\ \\ x=π/2$