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Question
Evaluate the following:
`cot^-1 1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`
Solution
`cot^-1 1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)=cot^-1(cot pi/3)-\text(cosec)^-1[\text(cosec)(-pi/6)]+sec^-1(sec pi/6)`
`=pi/3+pi/6+pi/6`
`=(2pi)/3`
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