A) \[\tan t\]
B) \[-\tan t\]
C) \[\cot t\]
D) \[-\cot t\]
Correct Answer: A
Solution :
Given that \[x=a\left( \cos t+\log \tan \frac{t}{2} \right)\] and \[y=a\sin t\]. Differentiating with respect to t, we get \[\frac{dy}{dt}=a\cos t\] .....(i) and \[\frac{dx}{dt}=a\left[ -\sin t+\cot \left( \frac{t}{2} \right)\,\left( \frac{1}{2} \right){{\sec }^{2}}\left( \frac{t}{2} \right) \right]\] \[=a\left( -\sin t+\frac{1}{\sin t} \right)=a\frac{{{\cos }^{2}}t}{\sin t}=a\cos t\cot t\] .....(ii) From (ii) and (i), we get \[\frac{dy}{dx}=\tan t\].
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