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  • Can someone explain - Limit , continuity and differentiability - JEE Main-11

Let x = \cos\theta, y = \sin\theta then  \frac{d^{2}y}{dx^{2}} = ?

  • Option 1)

    cosec ^{3}\theta

  • Option 2)

    - cosec ^{3}\theta

  • Option 3)

    \sin ^{3}\theta

  • Option 4)

    -\sin ^{3}\theta

 

Answers (1)

best_answer

As we have learnt,

 

Second order derivative for parametric function -

When we find 

\frac{dy}{dx}=F(t)\:then\:\frac{d^{2}y}{dx^{2}}=\frac{\frac{d}{dt}\:F(t)}{\frac{dx}{dt}}

-

 

 

\frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}= \frac{\frac{d}{d\theta}\sin\theta}{\frac{d}{d\theta}\cos\theta} = \frac{\cos\theta}{-\sin\theta} = -\cot \theta

\frac{d^2 y}{dx^2} = \frac{d}{dx}\left(\frac{dy}{dx} \right ) = \frac{\frac{d}{d\theta}(-\cot\theta)}{\frac{dx}{d\theta}} = \frac{cosec^2 \theta}{-\sin\theta} = -cosec^3\theta


Option 1)

cosec ^{3}\theta

Option 2)

- cosec ^{3}\theta

Option 3)

\sin ^{3}\theta

Option 4)

-\sin ^{3}\theta

Posted by

Himanshu

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