Question

If a = `sin^-1(sqrt2/2) + cos^-1(-1/2)` and b = `tan^-1 (sqrt3) - cot^-1(-1/sqrt3)` then find the value of a + b.

Answer 1

Since `a = sin^-1(sqrt2/2) + cos^-1((-1)/2)`

= `sin^-1(1/sqrt2) + cos^-1((-1)/2)`

= `pi/4 + (2pi)/3`

= `(11pi)/12`

`b = tan^-1(sqrt3) - cot^-1(-1/sqrt3)`

= `pi/3 - (2pi)/3`

= `(-pi)/3`

Now, a + b = `(11pi)/12 - pi/3`

= `(11pi - 4pi)/12`

= `(7pi)/12`