KCET · Maths · Differentiation
If \(y=a \sin ^3 t, x=a \cos ^3 t\), then \(\frac{d y}{d x}\) at \(t=\frac{3 \pi}{4}\) is
- A \(-1\)
- B \(\frac{1}{\sqrt{3}}\)
- C \(-\sqrt{3}\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
\(y=a \sin ^3 t, x=a \cos ^3 t\)
\(\begin{aligned} & \frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{3 a \sin ^2 t \cos t}{3 a \cos ^2 t(-\sin t)}=-\tan t \\ & t=\frac{3 \pi}{4}=1\end{aligned}\)
\(\begin{aligned} & \frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{3 a \sin ^2 t \cos t}{3 a \cos ^2 t(-\sin t)}=-\tan t \\ & t=\frac{3 \pi}{4}=1\end{aligned}\)
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