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Question
Find the principal value of the following:
`"cosec"^(-1)(-sqrt2)`
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Solution
Let `"cosec"^(-1)(-sqrt2)` = y
Then, cosec y = `-sqrt2 = - "cosec" (pi/4) = "cosec" (-pi/4)`
We know that the range of the principal value branch of cosec−1 is `[-pi/2,pi/2] - {0}` and `"cosec"(-pi/4) = -sqrt2`.
Therefore, the principal value of `"cosec"^(-1) (-sqrt2)` is `-pi/4`.
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