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प्रश्न
Find the value of the following:
`cos^(-1) (1/2) + 2 sin^(-1)(1/2)`
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उत्तर
We know that the range of the principal 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(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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