If the tangent to the curve y = x + sin y at a point a , b is parallel to the line joining 0 , 3 2 and 1 2 , 2 , then

Step-by-step solution

y = x + sin y d y d x = 1 + cos y d y d x d y d x = 1 1 - cos y Now for a ,   b ,   d y d x = 1 1 - cos b As the tangent is parallel to the line joining 0 ,   3 2 and 1 2 ,   2 ⇒ 1 1 - cos b = 2 - 3 2 1 2 - 0 ⇒    cos b = 0    ⇒    b = 2 n + 1 π 2 ,   n ∈ I Point lie on curve b = a + sin b b - a = sin b | b - a | = 1