Answer each of the following questions in one word or one sentence or as per exact requirement of the question:

Question

Answer each of the following questions in one word or one sentence or as per exact requirement of the question: Write the value of .

Philoid · Accepted Answer

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