Question

Evaluate:

`tan^(-1) [2sin(2cos^(-1)  (sqrt3)/2)]`

Answer 1

Given: `tan^(-1) [2sin(2cos^(-1)  (sqrt3)/2)]`

= `tan^(-1) [2sin(2 ⋅ pi/6)]     ...[∵ (cos^(-1)  (sqrt3)/2) = pi/6]`

= `tan^(-1) [2sin  pi/3]`

= `tan^(-1) [2 xx (sqrt3)/2]     ...(∵ sin  pi/3 = (sqrt3)/2)`

=  `tan^(-1) (sqrt3)`

= `pi/3`