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Question
Find the principal value of `cosec^(-1)(-sqrt2)`
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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