Question

Solve the equation.tan x = -1

Answer 1

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

Now to solve the above equation

$tan \: x = - 1 \\ \\ x = {tan}^{ - 1} ( - 1) \\ \\ x = tan - 1( - tan( \frac{\pi}{4} ) \\ \\ x = \pi - \frac{\pi}{4} \\ \\ x = \frac{4\pi - \pi}{4} \\ \\ x = \frac{3\pi}{4}$
because

${tan}^{ - 1} ( - x) = \pi - {tan}^{ - 1}x$