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If x = a(t + sint), y = a(1 – cost), then \frac{d y}{d x} \text { is : }

Option: 1

\tan \frac{t}{2}


Option: 2

\cot \frac{\mathrm{t}}{2}


Option: 3

\sec \frac{t}{2}


Option: 4

\operatorname{cosec} \frac{t}{2}


Answers (1)

best_answer

\begin{gathered} \frac{d x}{d t}=a(1+\cos t), \frac{d y}{d t}=a \sin t \\ \Rightarrow \quad \frac{d y}{d x}=\frac{d y}{d x} \cdot \frac{d t}{d x}=\frac{a \sin t}{a(1+\cos t)} \\ =\frac{2 \sin \frac{t}{2} \cos \frac{t}{2}}{2 \cos ^2 \frac{t}{2}}=\tan \frac{t}{2} \end{gathered}

Hence (A) is correct answer.

 

Posted by

Shailly goel

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