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# Solution for If Y = Sin (Sin X), Prove that D 2 Y D X 2 + Tan X ⋅ D Y D X + Y Cos 2 X = 0 ? - CBSE (Commerce) Class 12 - Mathematics

ConceptSimple Problems on Applications of Derivatives

#### Question

If y = sin (sin x), prove that $\frac{d^2 y}{d x^2} + \tan x \cdot \frac{dy}{dx} + y \cos^2 x = 0$ ?

#### Solution

Here,

$y = \sin\left( \sin x \right)$

$\text { Differentiating w . r . t . x, we get }$

$\frac{d y}{d x} = \cos\left( \sin x \right) \cos x$

$\text { Differentiating again w . r . t . x, we get }$

$\frac{d^2 y}{d x^2} = - \sin\left( \sin x \right) \cos^2 x - \cos\left( \sin x \right) \sin x$

$\Rightarrow \frac{d^2 y}{d x^2} = - \sin\left( \sin x \right) \cos^2 x - \cos\left( \sin x \right) \cos x\tan x$

$\Rightarrow \frac{d^2 y}{d x^2} = - y \cos^2 x - \tan x\frac{d y}{d x}$

$\Rightarrow \frac{d^2 y}{d x^2} + \tan x\frac{d y}{d x} + y \cos^2 x = 0$

Hence proved.

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Solution If Y = Sin (Sin X), Prove that D 2 Y D X 2 + Tan X ⋅ D Y D X + Y Cos 2 X = 0 ? Concept: Simple Problems on Applications of Derivatives.
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