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Question
The principal value of `sin^-1 [cos(sin^-1 1/2)]` is `pi/3`.
Options
True
False
Solution
This statement is True.
Explanation:
`sin^-1 [cos(sin^-1 1/2)] = sin^-1 [cos(sin^-1 sin pi/6)]`
`sin^-1 [cos pi/6] = sin^-1 (sqrt(3)/2)`
= `sin^-1 (sin pi/3)`
= `pi/3`
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