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Question

If 2 tan1(cos x)=tan1(2 cosec x) then the value of x is


  1. π/4

  2. 3π/4

  3. π/3

  4. π/8


Solution

The correct option is A

π/4


Given,
2 tan1(cos x)=tan1(2 cosec x)
tan1(2cos x1cos2x)=tan1(2 cosec x)
2cos x1cos2x=2 cosec x
2cos xsin2 x=2 cosec x
sin x=cos x
x=π4

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