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Explain solution for RD Sharma Class 12 Chapter 15 Tangent and Normals Exercise Very short Answers Question 19 for maths textbook solution.

Answers (1)

Answer : 0

Hint :

Simply we will find \frac{dy}{dx} at x = \frac{\pi }{6}


Given curve,

y=2 \sin ^{2} 3 x

We have to find the slope of the tangent to the given curve at x = \frac{\pi }{6}

Solution :

y=2 \sin ^{2} 3 x

Differentiating both sides with respect to x, we get

\begin{aligned} &\frac{d y}{d x}=2 \times 2 \sin (3 x) \times \cos (3 x) \times 3 \\ &\Rightarrow \quad\left(\frac{d y}{d x}\right)_{x=\frac{\pi}{6}}=12 \times \sin \left(\frac{\pi}{2}\right) \times \cos \left(\frac{\pi}{2}\right) \end{aligned}


\left(\frac{d y}{d x}\right)=0

Hence the slope of tangent = 0

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