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Question
Find the principal value of the following:
`tan^-1(cos pi/2)`
Solution
Let `tan^-1(cos pi/2)=y`
Then,
`tany=cospi/2`
We know that the range of the principal value branch is `(-pi/2,pi/2)`
Thus,
`tany=cos pi/2=0=tan(0)`
`=>y=0in(-pi/2,pi/2)`
Hence, the principal value of `tan^-1(cos pi/2)` is 0.
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