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AP EAMCET · Maths · Differentiation

If \(\frac{y}{x} \cos ^4 \alpha+\frac{x}{y} \sin ^4 \alpha=2 \sin ^2 \alpha \cdot \cos ^2 \alpha\), then \(\frac{d y}{d x}=\)

  1. A \(\sin ^3 \alpha \cos \alpha\)
  2. B \(\sin ^2 \alpha \cos ^2 \alpha\)
  3. C \(\frac{\sin ^2 \alpha}{\cos ^2 \alpha}\)
  4. D \(\sin \alpha \cos ^3 \alpha\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{\sin ^2 \alpha}{\cos ^2 \alpha}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { we have } \frac{\mathrm{y}}{\mathrm{x}} \cos ^4 \alpha+\frac{\mathrm{x}}{\mathrm{y}} \sin ^4 \alpha=2 \sin ^2 \alpha \cdot \cos ^2 \alpha \\ & \Rightarrow \mathrm{x}^2 \sin ^4 \alpha+\mathrm{y}^2 \cos ^4 \alpha-2 \mathrm{xy} \sin ^2 \alpha \cos ^2…