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  • Provide Solution for RD Sharma Class 12 Chapter 10 Differentiation Exercise 10.7 Question 3

Provide Solution for RD Sharma Class 12 Chapter 10 Differentiation Exercise 10.7 Question 3

Answers (1)

Answer:

            \frac{d y}{d x}=\frac{-b}{a} \cot \theta

Hint:

            \frac{d(\sin x)}{d x}=\cos x, \frac{d(\cos x)}{d x}=-\sin x

Given:

            x=a \cos \theta , y=b \sin \theta \\

Solution:

x=a \cos \theta

\\ \frac{d x}{d \theta}=-a \sin \theta \\

y=b \sin \theta \\

\begin{aligned} & &\frac{d y}{d \theta}=b \cos \theta \end{aligned}

\frac{d y}{d x}=\frac{\frac{d y}{d \theta}}{\frac{d x}{d \theta}}=\frac{b \cos \theta}{-a \sin \theta}=\frac{-b}{a} \cot \theta                                                                        \left[\because \cot \theta=\frac{\cos \theta}{\sin \theta}\right]

 

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