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Write the principal value of sin^(-1)...

Write the principal value of `sin^(-1)(-1/2)` .

Text Solution

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Let `y=cosec^(-1)(-2)`
`rArr cosecy=-2`
`:'` The principal values values of `cosec^(-1)x" lie in "[-pi/2,pi/2]-{0}`, and in this interval `cosec (-pi/6)=-2`
`:.cosec^(-1)(-2)=(-pi)/6`
`:.` The principal value of `cosec^(-1)(-2)=(-pi)/6`.
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