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Question
`"tan" ^-1 sqrt3 - "cot"^-1 (- sqrt3)` is equal to ______.
Options
π
`-pi/2`
0
`2 sqrt3`
Solution
`"tan" ^-1 sqrt3 - "cot"^-1 (- sqrt3)` is equal to `-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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