Question

Find value of k if `sin^-1 [k tan (2cos^-1  (sqrt3)/(2))] = pi/3`.

Answer 1

We have, `sin^-1 [k tan (2cos^-1  (sqrt3)/(2))] = pi/3`

`k [tan (2cos^-1 (cos  (pi)/(6)))] = sin  (pi)/3`

`k tan ((pi)/3) = sqrt3/2`

`k sqrt3 = sqrt 3/2`

k = `1/2`