A) \[\tan (t/2)\]
B) \[\cot (t/2)\]
C) \[\tan 2t\]
D) \[\tan t\]
Correct Answer: A
Solution :
\[\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{\frac{d}{dt}[a(1-\cos t)]}{\frac{d}{dt}[a(t+\sin t)]}\] \[\frac{dy}{dx}=\frac{a\sin t}{a+a\cos t}=\frac{\sin t}{1+\cos t}=\frac{2\sin \frac{t}{2}\cos \frac{t}{2}}{2{{\cos }^{2}}\frac{t}{2}}\] \[\therefore \frac{dy}{dx}=\tan \frac{t}{2}\].
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