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:
`cot theta`
`"We have, "x=3 cos theta -2 cos^(3)theta`
`"and "y=3 sin theta - 2 sin ^(3)theta`
`therefore" "(dx)/(d""theta)=-3 sin theta -2xx3 cos^(2) theta(d)/(d""theta)(cos theta)`
`=-3 sin theta + 6 cos^(2) theta sin theta`
`"And "(dy)/(d""theta)=3cos theta -2xx3sin^(2)theta(d)/(d""theta)(sin theta)`
`=3 cos theta -6 sin^(2) theta. cos theta`
`"Now, "(dy)/(dx)=(dy//d""theta)/(dx//d""theta)=(3cos theta-6 sin^(2)theta cos theta)/(-3 sin theta + 6cos^(2) theta sin theta)`
`=(3cos theta(1-2 sin^(2)theta))/(3 sin theta(-1+2cos^(2)theta))=cot theta. (cos 2theta)/(cos 2theta)=cot theta`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.5|16 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.6|8 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.3|8 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx) . x= cos theta-cos 2theta, y= sin theta-sin 2theta .

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

If x = 2costheta- cos 2theta, y = 2sintheta -sin 2theta, find dy/dx.

Solve 2 cos^(2) theta+3 sin theta=0

Find (dy)/(dx), " if "x= a cos theta, y= a sin theta .

Find (dy)/(dx)," if "x= a(theta+ sin theta), y= a(1- cos theta) .

If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx) . x= a (cos theta+ theta sin theta), y= a (sin theta-theta cos theta) .

Solve 3 cos^(2) theta=sin^(2) theta

Solve sqrt(3) cos theta-3 sin theta =4 sin 2 theta cos 3 theta .