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Question
The equation tan–1x – cot–1x = `(1/sqrt(3))` has ______.
Options
No solution
Unique solution
Infinite number of solutions
Two solutions
Solution
The equation tan–1x – cot–1x = `(1/sqrt(3))` has unique solution.
Explanation:
We have tan–1x – cot–1x = `pi/6` and tan–1x + cot–1x = `pi/2`
Adding them, we get 2tan–1x = `(2pi)/3`
⇒ tan–1x = `pi/3`
i.e., x = `sqrt(3)`.
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