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Question
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
Options
`pi/5`
`(2pi)/5`
`(3pi)/5`
`(4pi)/5`
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Solution
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is `(2pi)/5`.
Explanation:
We know tan–1x + cot–1x = `pi/2`.
Therefore cot–1x = `pi/2 - pi/10`
⇒ cot–1x = `pi/2 - pi/10 = (2pi)/5`.
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