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Question
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
Options
`pi/4`
`pi/3`
`pi/2`
`pi`
MCQ
Solution
`pi/4`
Explanation:
Given, `2tan^-1 (cosx) = tan^-1 (2"cosec" x)`
⇒ `tan^-1 ((2cos x)/(1 - cos^2x)) = tan^-1 (2"cosec" x)`
⇒ `(2 cos x)/(1 - cos^2x) = 2 "cosec" x`
⇒ `(2 cos x)/(sin^2 x) = 2/sinx`
⇒ `cos x = sin x`
⇒ `tan = 1`
⇒ `x = pi/4`
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