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Find (dy)/(dx) if x= 2 costheta- cos 2th...

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

Text Solution

Verified by Experts

The correct Answer is:
`(cos theta -2 cos 2 theta)/(2 sin 2 theta - sin theta)`
The given equations are `x=cos theta - cos 2 theta`
`and" "y = sin theta - sin 2theta`
`"Then, "(dx)/(d""theta)=-sin theta - (-2 sin 2theta)=2 sin 2 theta- sin theta`
`"And "(dy)/(d""theta)=cos theta -2 cos 2theta`
`therefore" "(dy)/(dx)=(dy//d""theta)/(dx//d""theta)=(cos theta-2 cos 2theta)/(2 sin 2theta- sin theta)`
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