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

Question

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, b = a, b - a = 1, a + b = 1, b = π 2 + a

MARKS App · Accepted Answer

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

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