Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 12 maths

Explain solution RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 12 maths

Answers (1)

Answer:

        \frac{32}{27a}

Hint:

You must know about derivative of

        \frac{cos^{3}\theta}{sin^{3}\theta }

Given:

\begin{aligned} &{\text { If } x=a\left(1-\cos ^{3} \theta\right), y=a \sin ^{3} \theta} \\ &\text { Prove that } \frac{d^{2} y}{d x^{2}}=\frac{32}{27 a} \; a t\; \theta=\frac{\pi}{6} \end{aligned}

Solution:

\begin{aligned} &{\text { Let } x=a\left(1-\cos ^{3} \theta\right), y=a \sin ^{3} \theta} \end{aligned}

        \begin{aligned} &\frac{d y}{d \theta}=3 a \sin ^{2} \theta \cos \theta\left(\frac{d}{d \theta} \sin ^{3} \theta=3 a \sin ^{2} \theta \cos \theta\right) \\ &\frac{d y}{d \theta}=3 \cos ^{2} \theta \sin \theta \ \left(\frac{d}{d \theta} \cos ^{3} \theta=3 \cos ^{2} \theta \sin \theta\right) \\ &\frac{d y}{d x}=\tan \theta \quad \quad\left(\frac{d}{d \theta} \tan \theta=\sec ^{2} \theta\right) \end{aligned}

        \begin{aligned} &\frac{\frac{d}{d \theta}\left(\frac{d y}{d x}\right)}{\frac{d x}{d \theta}}=\frac{\sec ^{2} \theta}{3 a \cos ^{2} \theta \sin \theta}\\ &\frac{d^{2} y}{d x^{2}}=\frac{\sec ^{4} \theta}{3 a \sin \theta} \quad\left(\theta=\frac{\pi}{6}\right)\\ &\frac{d^{2} y}{d x^{2}}=\frac{\sec ^{4}\left(\frac{\pi}{6}\right)}{3 a \sin \left(\frac{\pi}{6}\right)}=\frac{32}{27 a} \end{aligned}

Hence proved

Posted by

Gurleen Kaur

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 Board Economics Paper Analysis: 'Student-friendly', well balanced with moderate difficulty
anam-khan

CBSE Class 12 Hindi exam 2025 not postponed; special exam for those who miss
anam-khan

CBSE Board Exams 2025 LIVE: Class 12 Hindi paper over; updates on exam analysis, answer key

Latest Question