Question

For the principal value, evaluate of the following:

`cos^-1  1/2 + 2 sin^-1 (1/2)`

Evaluate: `cos^-1 (1/2) + 2 sin^-1 (1/2)`

Answer 1

cos^–1 (cos x) = x

sin^–1 (sin x) = x

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

= `cos^-1 (cos  π/3) + 2 sin^-1 (sin  π/6)`

= `π/3 + 2(π/6)`

= `(2π)/3`