Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 Chapter 15 Tangents and Normals Exercise Very Short Answer Question 10 maths text book solution.

Provide solution for RD Sharma maths class 12 Chapter 15 Tangents and Normals Exercise Very Short Answer Question 10 maths text book solution.

Answers (1)

Answer : Equation of normal =2x = \pi

Hint : Use equation of normal,

          y-y_{1}=\frac{1}{\frac{d y}{d x}}\left(x-x_{1}\right)

Given :

Here given that the curve

    y=x+\sin x \cos x

We have to write the equation of normal to the given curve at x=\frac{\pi }{2}

Solution:

We have,

y=x+\sin x \cos x

On differentiating both sides with respect to  'x', we get

\frac{d y}{d x}=1+\cos ^{2} x-\sin ^{2} x

Now we know that,

\begin{aligned} &\text { slope of tangent }=\left(\frac{d y}{d x}\right)_{x=\frac{\pi}{2}} \\ &=1+\cos ^{2}\left(\frac{\pi}{2}\right)-\sin ^{2}\left(\frac{\pi}{2}\right) \\ &=1+0-1 \\ &=0 \end{aligned}

Now,

When x=\frac{\pi}{2} \Rightarrow y=\frac{\pi}{2}+\sin \frac{\pi}{2} \cos \frac{\pi}{2}

\Rightarrow y=\frac{\pi }{2}

\therefore \quad\left(x_{1}, y_{1}\right)=\left(\frac{\pi}{2}, \frac{\pi}{2}\right)

So, equation of normal

          \begin{aligned} &y-y_{1}=\frac{-1}{\text { slope of tangent }}\left(x-x_{1}\right) \\ &y-\frac{\pi}{2}=\frac{-1}{0}\left(x-\frac{\pi}{2}\right) \end{aligned}

\begin{array}{ll} \Rightarrow \quad & x=\frac{\pi}{2} \\ \Rightarrow & 2 x=\pi \end{array}

Hence the equation of the given curve at x=\frac{\pi}{2} \text { is } 2 x=\pi.

 

Posted by

infoexpert23

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 10, 12 compartment 2024 exams today for 2.5 lakh students; exam timings, guidelines
anam-khan

CBSE compartment admit card 2024 out at cbse.gov.in; exams from July 15
anam-khan

Reports saying CBSE cannot conduct board exams twice a year currently ‘totally incorrect’; board denies claims

Latest Question