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Cosec2tan-1(cosx)=tan-1(2cosec x), then 'x' will be equal to -

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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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