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Question
Find the principal values of the following:
`cos^-1(-1/sqrt2)`
Solution
Let `cos^-1(-1/sqrt2) = y`
Then,
`cosy=-1/sqrt2`
We know that the range of the principal value branch is [0, π].
Thus,
`cosy=-1/sqrt2=cos((3pi)/4)`
`=>y=(3pi)/4 in[0,pi]`
Hence, the principal value of `cos^-1(-1/sqrt2) is (3pi)/4`
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