Question

If `2sin^-1  3/7` = cos^–1β, then find the value of β.

Answer 1

To find the value of `2sin^-1  3/7`

Let `sin^-1  3/7` = θ,

∴ sin θ = `3/7`

Consider cos 2θ = 1 – 2 sin²θ

= `1 - 2(9/49)`

= `(49 - 18)/49`

= `31/49`

∴ 2θ = `cos^-1  31/49`

i.e. `2sin^-1  3/7 = cos^-1  31/49`

∴ β = `31/49`