Solve this


Find $\frac{\mathrm{dy}}{\mathrm{dx}}$, when

If $x=10(t-\sin t), y=12(1-\cos t)$, find $\frac{d y}{d x}$


Here, $x=10(t-\sin t) y=12(1-\cos t)$

$\frac{\mathrm{dx}}{\mathrm{dt}}=10(1-\cos \mathrm{t})$     (1)

$\frac{d y}{d t}=12(\sin t) \ldots \ldots(2)$             

$\frac{d y}{d x}=\frac{\frac{d y}{d x}}{\frac{d x}{d t}}=\frac{12(\sin t)}{10(1-c o s t)} \mid$ from equation 1 and 2

$\frac{d y}{d x}=\frac{12 \sin \frac{t}{2} \cdot \cos t / 2}{10 \sin ^{2} t / 2}$

$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{6}{5} \cot \frac{\mathrm{t}}{2}$

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now