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