COMEDK · Maths · 26. Differentiation
If \(x=a\left(\cos t+\log \tan \frac{t}{2}\right), y=a \sin t\), then \(\frac{d y}{d x}=\)
- A \(\tan t\)
- B \(\cot t\)
- C \(-\cot t\)
- D \(\tan t\)
Answer & Solution
Correct Answer
(D) \(\tan t\)
Step-by-step Solution
Detailed explanation
We have, \[ x=a\left(\cos t+\log \tan \frac{t}{2}\right) \] Now, \(\frac{d x}{d t}=a\left\{-\sin t+\frac{1}{\tan \frac{t}{2}} \cdot \sec ^{2} \frac{t}{2} \cdot \frac{1}{2}\right\}\) \[ =a\left\{-\sin t+\frac{1}{\sin t}\right\} \]…
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