AP EAMCET · Maths · Differentiation
If \(y=4 \cos ^3(t)\) and \(x=4 \sin ^3(t)\), then \(\frac{d y}{d x}\) is equal to
- A \(-\tan (t)\)
- B \(\tan (t)\)
- C \(-\cot (t)\)
- D \(\cot (t)\)
Answer & Solution
Correct Answer
(C) \(-\cot (t)\)
Step-by-step Solution
Detailed explanation
\(y=4 \cos ^3(t)\) and \(x=4 \sin ^3 9(t)\) \(\begin{aligned} & \therefore \quad \frac{d y}{d t}=4 \cdot 3 \cdot \cos ^2 t(-\sin t)=-12 \sin t \cos ^2 t \\ & \text { and } \frac{d x}{d t}=4 \cdot 3 \cdot \sin ^2 t \cdot \cos t=12 \sin ^2 t \cdot \cos t\end{aligned}\)…
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