Write the value of cos^-1(1/2) + 2 sin^-1(1/2).

Question

Write the value of cos^-1(\(\frac 12\)) + 2 sin^-1(\(\frac 12\)).

Answer 1

Let cos^-1(1/2) = x and sin ^-1 (1/2) = y

⇒ cos x = 1/2 and sin y = 1/2

We know that the range of the principal value branch of sin^-1 is (-π/2, π/2) and cos^-1 is (0, π).

We also know that sin (π/ 6) = 1/2 and cos (π/3) = 1/2

⇒ Value of cos^-1 (1/2) + 2sin^-1 (1/2) = π/3 + 2(π/6)

= π/3 + π/3

= 2π/3

∴ Value of cos^-1 (1/2) + 2sin^-1 (1/2) = 2π/3