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


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