If `x= a sin 2theta (1+ cos 2theta)`, `y= b cos 2theta(1- cos 2theta)`, then `(dy)/(dx)`=

Explanation

` x asin 2 theta (1 + cos 2 theta) = a [ sin 2 theta + ( sin 4theta)/2]`
` Rightarrow (dx)/(d theta) =a[ 2 cos 2 theta + 2 cos 4 theta ]`
` 2a[ cos 2 theta + cos 4 theta] = 4 a cos theta cos 3 theta`
` and y= b cos 2 theta (1-cos theta) = b(cos^(2) 2theta) = b ( cos2 theta - 1/2 - (cos 4 theta)/2)`
`= 4 b cos 3 theta sin theta`
Hence ` (dy)/(dx) = ((dy)/(d theta))/(dx/(d theta)) = (4 b cos 2 theta sin theta)/(4 a cos theta cos 3 theta) = b/a tan theta`