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Question
Find the value of the given expression.
`sin^(-1) (sin (2pi)/3)`
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Solution
We know that sin–1 (sin x) = x if `x ∈ [-pi/2, pi/2]`, which is the principal value branch of sin–1 x.
Here, `(2pi)/3 ∉ [(-pi)/2, pi/2]`
Now, `sin^(-1) (sin (2pi)/3)` can be written as:
`sin^(-1) (sin (2pi)/3) `
= `sin^(-1) [sin (pi - (2pi)/3)] `
= `sin^(-1) (sin pi/3)` where `pi/3 ∈ [(-pi)/2, pi/2]`
∴ `sin^(-1) (sin (2pi)/2)`
= `sin^(-1) (sin pi/3) `
= `pi/3`
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