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Question
`tan^-1 sqrt3 - cot^-1 (- sqrt3)` is equal to ______.
Options
π
`-pi/2`
0
`2 sqrt3`
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Solution
`tan^-1 sqrt3 - cot^-1 (- sqrt3)` is equal to `underlinebb(-pi/2)`.
Explanation:
⇒ `tan^-1 sqrt3 - cot^-1 (- sqrt3)`
= `tan^-1 (tan pi/3) - cot^-1 (-cot pi/6)`
= `pi/3 - cot^-1 [cot (pi - pi/6)]`
= `pi/3 - cot^-1 [cot ((5pi)/6)]`
= `pi/6 - (5 pi)/6`
= `(2pi - 5pi)/6`
= `-(3pi)/6`
= `- pi/2`
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