Search any question & find its solution
Question:
Answered & Verified by Expert
If $x=a(t-\sin t)$ and $y=a(1-\cos t)$, then $\frac{d y}{d x}=$
Options:
Solution:
2670 Upvotes
Verified Answer
The correct answer is:
$\cot \left(\frac{t}{2}\right)$
\(\begin{aligned}
\Rightarrow \text { So, } \frac{d y}{d t} & =\frac{d}{d t}(a(1-\cos t))=a \cdot \sin t \\
\frac{d x}{d t} & =\frac{d}{d t}(a(t-\sin t))
\end{aligned}\)
So, \(\frac{d y}{d x}=\frac{a \sin t}{a(1-\cos t)}=a(1-\cos t)\)
\(=\frac{2 \sin (t / 2) \cdot \cos (t / 2)}{2 \sin ^2(t / 2)}=\cot (t / 2)\)
\Rightarrow \text { So, } \frac{d y}{d t} & =\frac{d}{d t}(a(1-\cos t))=a \cdot \sin t \\
\frac{d x}{d t} & =\frac{d}{d t}(a(t-\sin t))
\end{aligned}\)
So, \(\frac{d y}{d x}=\frac{a \sin t}{a(1-\cos t)}=a(1-\cos t)\)
\(=\frac{2 \sin (t / 2) \cdot \cos (t / 2)}{2 \sin ^2(t / 2)}=\cot (t / 2)\)
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.