Question

Find $\frac{dy}{dx}$, if $x=\cos \theta -\cos 2\theta$, $y=\sin \theta -\sin 2\theta$

Answer 1

Given $x=\cos \theta -\cos 2\theta$ …………..$\left(1\right)$

$y=\sin \theta -\sin 2\theta$ …………$\left(2\right)$

Differentiating equation $\left(1\right)$ & $\left(2\right)$ w.r.t. $\theta$.

$\frac{dx}{d\theta }=-\sin \theta +2\sin 2\theta$

$\frac{dy}{d\theta }=\cos \theta -2\cos 2\theta$

Now $\frac{\frac{dy}{d\theta }}{\frac{dx}{d\theta }}=\frac{\cos \theta -2\cos 2\theta }{2\sin 2\theta -\sin \theta }$.