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Question
If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is ______.
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Solution
If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is `sqrt(3)`.
Explanation:
We have, `cos(tan^-1x + cot^-1 sqrt(3))` = 0
⇒ `tan^-1x + cot^-1 sqrt(3) = cos^-1 0`
⇒ `tan^-1x + cot^-1 sqrt(3) = pi/2`
⇒ `tan^-1x = pi/2 - cot^-1 sqrt(3)`
⇒ `tan^-1x = tan^-1 sqrt3)` .....`(because tan^-1x + cot^-1x = pi/2)`
∴ x = `sqrt(3)`
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