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Question
Find the value of the following:
`cos^(-1) (1/2) + 2 sin^(-1)(1/2)`
Solution
We know that the range of principlal value branch of cos-1 and sin-1 are [0, π] and `[-pi/2, pi/2]` respectively.
Let `cos^(-1) (1/2) = x`
= `1/2 = cos x,`
Then, `1/2 = cos (pi/3), "where" pi/3 ∈ [0, pi]`
Let `sin^(-1) (1/2) = y`
= `1/2 = sin y`
then, `1/2 = sin = y (pi/6), "where" pi/6 ∈ [-pi/2, pi/2]`
∴ `cos^(-1) (1/2) + 2sin^(-1) (1/2) = pi/3 + 2* pi/6`
= `pi/3 + pi/3 = (2pi)/3`
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