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Question
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)-2sec^-1(2tan pi/6)`
Solution
`sin^-1(-sqrt3/2)-2sec^-1(2tan pi/6)=-sin^-1(sqrt3/2)-2sec^-1(2xx1/sqrt3)`
`=-sin^-1(sqrt3/2)-2sec^-1(2/sqrt3)`
`=-sin^-1(sin pi/3)-2sec^-1(sec pi/6)`
`=-pi/3-pi/3`
`=-(2pi)/3`
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