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Solution for Find the Slope of the Tangent and the Normal to the Following Curve at the Indicted Point Y = (Sin 2x + Cot X + 2)2 at X = π/2 ? - CBSE (Science) Class 12 - Mathematics

Question

Find the slope of the tangent and the normal to the following curve at the indicted point  y = (sin 2x + cot x + 2)2 at x = π/2 ?

Solution

$y = \left( \sin 2x + \cot x + 2 \right)^2$

$\Rightarrow \frac{dy}{dx} = 2 \left( \sin 2x + \cot x + 2 \right) \left( 2\cos 2x - \cose c^2 x \right)$

$\text { Now,}$

$\text { Slope of the tangent }= \left( \frac{dy}{dx} \right)_{x = \frac{\pi}{2}}$

$=2\left[ \sin 2\left( \frac{\pi}{2} \right) + \cot \left( \frac{\pi}{2} \right) + 2 \right] \left[ 2\cos 2\left( \frac{\pi}{2} \right) - {cosec}^2 \left( \frac{\pi}{2} \right) \right]$

$= 2 \left( 0 + 0 + 2 \right) \left( - 2 - 1 \right)$

$= - 12$

$\text { Slope of the normal }=\frac{- 1}{\left( \frac{dy}{dx} \right)_{x = \frac{\pi}{2}}}=\frac{- 1}{- 12}=\frac{1}{12}$

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Solution Find the Slope of the Tangent and the Normal to the Following Curve at the Indicted Point Y = (Sin 2x + Cot X + 2)2 at X = π/2 ? Concept: Tangents and Normals.
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