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Question
Find the principal value of the following:
cosec-1(-2)
Solution
Let cosec-1(-2) = y
Then,
cosec y = -2
We know that the range of the principal value branch is `[-pi/2,pi/2]-{0}.`
Thus,
cosec y = -2 = `cosec(-pi/6)`
`y=-pi/6in[-pi/2,pi/2],y!=0`
Hence, the principal value of `cosec^-1(-2) is -pi/6`
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