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Question
If 3 tan–1x + cot–1x = π, then x equals ______.
Options
0
1
– 1
`1/2`
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Solution
If 3 tan–1x + cot–1x = π, then x equals 1.
Explanation:
Given that 3 tan–1x + cot–1x = π
⇒ 2 tan–1x + tan–1x + cot–1x = π
⇒ `2 tan^-1x + pi/2` = π ......`[because tan^-1x + cot^-1x = pi/2]`
⇒ `2tan^-1x = pi - pi/2`
⇒ `2tan^-1x = pi/2`
⇒ `2tan^-1x = pi/4`
⇒ `tan^-1x = tan^-1(1)`
⇒ x = 1
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