Continuity and Differentiability Question - CBSE

Question

If $\sin y = x \sin(a + y)$, prove that $\dfrac{dy}{dx} = \dfrac{\sin^2(a + y)}{\sin a}$.

Accepted Answer

Express $x = \dfrac{\sin y}{\sin(a+y)}$. [1.0 Mark]
$\dfrac{dx}{dy} = \dfrac{\sin a}{\sin^2(a+y)}$. [1.0 Mark]
Taking reciprocal: $\dfrac{dy}{dx} = \dfrac{\sin^2(a+y)}{\sin a}$. Proved! [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Expressing $x$ as function of $y$: 1.0 Mark
Differentiating $dx/dy$ using Quotient Rule: 1.0 Mark
Inverting to obtain $dy/dx$: 1.0 Mark

Question:

Step-by-Step Solution

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