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Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .
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
∴ Value of cos-1 (1/2) + 2sin-1 (1/2) = 2π/3