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प्रश्न
Find the principal value of the following:
`cosec^-1(-sqrt2)`
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उत्तर
Let `cosec^-1(-sqrt2)=y`
Then,
`cosecy=-sqrt2`
We know that the range of the principal value branch is `[-pi/2,pi/2]-{0}`.
Thus,
`cosecy=-sqrt2=cosec(-pi/4)`
`y=-pi/4in [-pi/2,pi/2],y!=0`
Hence, the principal value of `cosec^-1(-sqrt2) is -pi/4.`
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