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Question
`cos^(-1) (cos (7pi)/6)` is equal to ______.
Options
`(7pi)/6`
`(5pi)/6`
`pi/3`
`pi/6`
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Solution
`cos^(-1) (cos (7pi)/6)` is equal to `underlinebb((5pi)/6)`.
Explanation:
`cos^(-1) (cos (7pi)/6) ≠ (7pi)/6` as the principal value branch of cos−1 is [0, π].
∴ `cos^(-1) (cos (7pi)/6)`
= `cos^(-1) (cos (pi + pi/6))`
= `cos^-1(-cos pi/6)`
= `cos^-1 (cos(pi - pi/6))`
= `(5pi)/6`
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