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