If the tangent to the curve y = x + sin y .npoint( a, b) is para/le/to the line joining (0, 3/2) and (1/2, 2), then

If the tangent to the curve y = x + sin y .npoint( a, b) is para/le/to the line joining (0, 3/2) and (1/2, 2), then

  1. A

    |ba|=1

  2. B

    b=π2+a

  3. C

    |a+b|=1

  4. D

    b=a

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    Solution:

    We have, y=x+siny

    dydx=1+cosydydxdydx=11cosydydx(a,b)=11cosb

    lt is given that the tangent at (a, b) is parallel to the line joinin
    (0, 3/2) and (1/2, 2).

     dydx(n,b)=23/21/20 11cosb=1cosb=0b=(2n+1)π2,nZ

    Point (a, b) lies on y = x + sin y

     b=a+sinbb=a+sin(2n+1)π2 ba=sin(2n+1)π2ba=±1|ba|=1

     

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