Write the principal value of

We know that:

tan^-1x + cot^-1x = π/2

and cot^-1(-x) = π – cot^-1 x

∴ tan^-1(√3) - cot^-1(-√3) = tan^-1(√3) –{π - cot^-1(√3)}

⇒ tan^-1(√3) - cot^-1(-√3) = -π + tan^-1(√3) + cot^-1(√3)

⇒ tan^-1(√3) - cot^-1(-√3) = -π + π/2 = -π/2

∴ tan^-1(√3) - cot^-1(-√3) = -π/2