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Explain solution for RD Sharma maths Class 12 Chapter 15 Tangents and Normals Exercise Multiple Choice Question, Question 32 maths textbook solution.

Answers (1)

Answer : (d) is the correct option

Hint :

\text { Put } t=\frac{\pi}{4} \text { in } \frac{d y}{d x}

Given : x=e^{t} \cos t, y=e^{t} \sin t

Solution :

x=e^{t} \cos t                                                (1)

Differentiating (1) w.r.t t, we get

\begin{aligned} &\frac{d x}{d y}=e^{t}(\cos t-\sin t) \\ &y=e^{t} \sin t \end{aligned}                          (2)

Differentiating (2) w.r.t t, we get

\begin{aligned} &\frac{d y}{d t}=e^{t}(\cos t+\sin t) \\ &\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{\cos t+\sin t}{\cos t-\sin t} \end{aligned}

\begin{aligned} &{\left[\frac{d y}{d x}\right]_{(0,0)}=\infty} \\ &\tan ^{-1}(\infty)=\frac{\pi}{2} \end{aligned}


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