The angle between the curves y=sin⁡x and y=cos⁡x0

The angle between the curves y=sinx and y=cosx

0<x<π2, is

  1. A

    tan1(22)

  2. B

    tan1(32)

  3. C

    tan1(33)

  4. D

    tan1(52)

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    Solution:

    Curves y = sin x and y = cos x intersect at

    P(π/4,12)

    Now,

    y=sinxdydx=cosxm1=dydxP=cosπ4=12y=cosxdydx=sinxm2=dydxρ=sinπ4=12

    Let θ be the angle between the given curves at P. Then, 

    tanθ=m1m21+m1m2 tanθ=2112=220=tan1(22)

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