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Question
Evaluate the following:
`tan^-1(-1/sqrt3)+cot^-1(1/sqrt3)+tan^-1(sin(-pi/2))`
Solution
`tan^-1(-1/sqrt3)+cot^-1(1/sqrt3)+tan^-1(sin(-pi/2))=tan^-1[tan(-pi/6)]+cot^-1(cot pi/3)+tan^-1(-1)`
`=tan^-1[tan(-pi/6)]+cot^-1(cot pi/3)+tan^-1[tan(-pi/4)]`
`=-pi/6+pi/3-pi/4`
`=-pi/12`
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