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Question
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)+\text{cosec}^-1(-2/sqrt3)`
Solution
`sin^-1(-sqrt3/2)+cosec^-1(-2/sqrt3)=-sin^-1(sqrt3/2)+cosec^-1(-2/sqrt3)`
`=-sin^-1(sin pi/3)+cosec^-1[cosec(-pi/3)]`
`=-pi/3-pi/3`
`=-(2pi)/3`
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