If x∈(1,∞), then sin−1⁡2×1+x2 equals

If x(1,), then sin12x1+x2 equals

  1. A

    2 tan1x

  2. B

    π -2 tan1x

  3. C

    -π -2 tan1x

  4. D

    none of these

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    Solution:

    Let tan1x=θ. Then, x=tanθ

    Now,

           x(1,)tanθ>1π4<θ<π2π2<2θ<π

     sin12x1+x2     = sin1(sin2θ)     = sin1(sin(π2θ))

         = π2θ π4<θ<π2π2<π2θ<0

          =π2tan1x

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