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Provide solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 18

Answers (1)




You must know about derivative of

        cos\: \theta\: and\: tan\: \theta


        I\! f\: y=sin(sin\: x)

        \begin{aligned} &Prove\: \: that\: \: \frac{d^{2} y}{d x^{2}}+\tan x \frac{d y}{d x}+y \cos ^{2} x =0\\ \end{aligned}


Let\: y=sin(sin\: x)

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

        \begin{aligned} &L H S:-\frac{d^{2} y}{d x^{2}}+\tan x \frac{d y}{d x}+y \cos ^{2} x \\ &-\sin x \cos (\sin x)-\cos ^{2} x(\sin (\sin x))+\tan x \cos x \cos (\sin x)+\sin (\sin x) \cos ^{2} x \\ &-\sin x(\cos (\sin x))+\frac{\sin x}{\cos x} \cdot \cos x \cdot \cos (\sin x) \\ &-\sin x \cos x \sin x+\sin x \cos x \sin x \end{aligned}

Hence proved

Posted by

Gurleen Kaur

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