Home
Class 12
MATHS
Find (dy)/(dx) if x=3 cos theta- 2cos^(3...

Find `(dy)/(dx) if x=3 cos theta- 2cos^(3)theta,y=3 sin theta -2sin^(3) theta.`

Text Solution

Verified by Experts

The correct Answer is:
N/a
`:' x=3costheta-2cos^(3)theta` and ` y = 3sin theta - 2 sin^(3) theta`
`:. (dx)/(dy) = (d)/(dx) (3cos theta)-(d)/(d theta)(2cos^(3) theta)`
`= 3.(-sin theta)-2.3 cos^(2) theta.(d)/(d theta). cos theta`
`= -3 sin theta+ 6 cos^(2) theta sin theta`
and `(dy)/(d theta) = 3 cos A - 2.3 sin^(2) theta.(d)/(d theta) . sin theta`
`= 3 cos theta - 6 sin^(2) theta.costheta`
Now, `(dy)/(dx) = (dy//d theta)/(dx//d theta)= (3costheta-6sin^(2) thetacostheta)/(-3sin theta+6cos^(2) thetasin theta)`
`= (3costheta(1-2sin^(2) theta))/(3sin theta(-1+2cos^(2) theta)) = cot theta. (cos2 theta)/(cos 2 theta) = cot theta`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT EXEMPLAR ENGLISH|Exercise Objective type|28 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT EXEMPLAR ENGLISH|Exercise Fillers|10 Videos

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR ENGLISH|Exercise Objective Type Questions|22 Videos

  • DETERMINANTS

    NCERT EXEMPLAR ENGLISH|Exercise TRUE/FALSE|11 Videos

Similar Questions

Explore conceptually related problems

Find (dy)/(dx) if x= 3 cos theta - cos 2theta and y= sin theta - sin 2theta.

Find (dy)/(dx) if x=cos theta - cos 2 theta and" "y = sin theta - sin 2theta

If x=3costheta-cos^3theta y=3sintheta-sin^3theta find dy/dx

If x = 3 cos theta - 2 cos^3 theta,y = 3 sin theta - 2 sin^3 theta , then dy/dx is

cos theta+sqrt(3)sin theta=2

The roots of the equation |(3x^(2),x^(2) + x cos theta + cos^(2) theta ,x^(2) + x sin theta + sin^(2) theta),(x^(2) + x cos theta + cos^(2) theta,3 cos^(2) theta,1 + (sin 2 theta)/(2)),(x^(2) + x sin theta + sin^(2) theta,1 + (sin 2 theta)/(2),3 sin^(2) theta)| = 0

sin^(3)theta + sin theta - sin theta cos^(2)theta =

cos ^(2) 2 theta - sin ^(2) theta = cos theta . cos 3 theta.

If 2 cos theta = sqrt3. prove that : 3 sin theta - 4 sin ^(3) theta =1

Find dy/dx x=a\ cos^3theta , y=a\ sin^3theta