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Question
If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals ______.
Options
`pi/5`
`(2pi)/5`
`(3pi)/5`
π
Solution
If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals `pi/5`.
Explanation:
We have, tan–1x + tan–1y = `(4pi)/5`
⇒ `pi/2 - cot^-1x + pi/2 - cot^-1y = (4pi)/5`
⇒ `pi- (cot^-1x + cot^-1y) = (4pi)/5` .....`(because tan^-1x + cot^-1x = pi/2)`
⇒ `cot^-1x + cot^-1y = pi - (4pi)/5`
⇒ `cot^-1x + cot^-1y = pi/5`
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