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प्रश्न
`cos^(-1) (cos (7pi)/6)` is equal to ______.
पर्याय
`(7pi)/6`
`(5pi)/6`
`pi/3`
`pi/6`
उत्तर
`cos^(-1) (cos (7pi)/6)` is equal to `(5pi)/6`.
Explanation:
`"cos"^-1 ("cos" (7pi)/6) "x" in [0, pi]`
`Rightarrow "cos"^-1 ("cos" (7 pi)/6) = "cos"^-1 ("cos" (-7pi)/6)`
`= "cos"^-1 ("cos" (2 pi - (7pi)/6))`
`Rightarrow "cos"^-1 ["cos" (5 pi)/6] "where" (5pi)/6 in [0, pi]`
`Rightarrow therefore "cos"^-1 ("cos" (7pi)/6) `
`= "cos"^-1 ["cos" (5pi)/6]`
` = (5pi)/6`
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