Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please solve RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 17 maths textbook solution

Please solve RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 17 maths textbook solution

Answers (1)

Answer:

\begin{aligned} &\text { } 3 \sin ^{2} \theta\left[5 \cos ^{2} \theta-1\right]\\ \end{aligned}

Hint:

\begin{aligned} &\text { You must know about derivative of } \cos \theta\: \&\: \sin \theta\\ \end{aligned}

Given:

\begin{aligned} &\text { If } x=\cos \theta, y=\sin ^{3} \theta\\ &\text { Prove that } y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=3 \sin ^{2} \theta\left[5 \cos ^{2} \theta-1\right] \end{aligned}

Solution:

\begin{aligned} &\text { Let } x=\cos \theta, y=\sin ^{3} \theta\\ \end{aligned}

        \begin{aligned} &\frac{d x}{d \theta}=-\sin \theta \\ &\frac{d y}{d \theta}=3 \sin ^{2} \theta \cos \theta \\ &\frac{d y}{d x}=\frac{\frac{d y}{d \theta}}{\frac{d x}{d \theta}}=\frac{3 \sin ^{2} \theta \cos \theta}{-\sin \theta}=3 \sin \theta \cos \theta \end{aligned}

        \begin{aligned} &\frac{d^{2} y}{d x^{2}}=d\left(\frac{\frac{d y}{d x}}{d x}\right)=\frac{d\left(\frac{d y}{d \theta}\right) d \theta}{\frac{d x}{d \theta}} \\ &=\frac{-\cos ^{2} \theta \cdot 3+3 \sin ^{2} \theta}{-\sin \theta} \end{aligned}

        \begin{aligned} &y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=\frac{\sin ^{3} \theta\left(3 \cos ^{2} \theta-3 \sin ^{2} \theta\right)}{\sin \theta} \\ &y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=3 \sin ^{2} \theta\left[5 \cos ^{2} \theta-1\right] \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

Board Exam Time Table 2027 LIVE: Bihar, Assam, Gujarat Class 10, 12 dates soon; practicals, syllabus updates
anam-khan

CBSE Date Sheet 2027 (OUT) LIVE: Class 10, 12 exam dates out for over 46 lakh students; passing marks
anam-khan

CBSE Class 12 exams clash with Holi on March 22; will board revise date sheet?

Latest Question