Question

Find the value of `tan^-1 (sqrt(3)) - sec^-1 (- 2)`

Answer 1

x = `tan^-1 (sqrt(3))`

tan x = `sqrt(3) = tan  pi/3`

x = `pi/3`

y = `sec^-1(- 2)`

sec y = ` - 2 = - sec  pi/3`

sec y = `sec(pi - pi/3)`

sec y = `sec(2 pi/3)`

y = `(2  pi/3)`

`tan^-1 (sqrt(3)) - sec^-1(- 2) = pi/3 - (2pi)/3`

= `(pi - 2pi)/3`

= `- pi/3`