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Question
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
Solution
Let `cos^-1(-sqrt3/2) = y`
Then,
`cosy=-sqrt3/2`
We know that the range of the principal value branch is [0, π].
Thus,
`cosy=-sqrt3/2=cos((5pi)/6)`
`=>y=(5pi)/6in[0,pi]`
Hence, the principal value of `cos^-1(-sqrt3/2)` is `(5pi)/6.`
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