IGNOU MTE 1 2018 - If x sin y = sin (p + y), p ∈ R, show that sin p dy/dx + sin 2 y

Question

If x sin y = sin (p + y), p ∈ R, show that sin p dy/dx + sin² y = 0.

01 Feb 2018

Answer :

Word Count : 260

To solve this equation, let's first express the given equation and then find the derivative step by step. Given: \[ x \sin(y) = \sin(p + y) \] Now, differentiate both sides with respect to \( x \) using implicit differentiation. ### Step 1: Differentiate both sides of the equation 1. Left-hand side (LHS): \[ \frac{d}{dx}(x \sin(y)) = \sin(y) \frac{dx}{dx} + x \cos(y) \frac{dy}{dx} = \sin(y)

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