AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(x+\frac{1}{x}=2 \sin \alpha\) and \(y+\frac{1}{y}=2 \cos \beta\), then \(x^3 y^3+\frac{1}{x^3 y^3}=\)
- A \(2 \cos 3(\beta-\alpha)\)
- B \(2 \cos 3(\beta+\alpha)\)
- C \(2 \sin 3(\beta-\alpha)\)
- D \(2 \sin 3(\beta+\alpha)\)
Answer & Solution
Correct Answer
(C) \(2 \sin 3(\beta-\alpha)\)
Step-by-step Solution
Detailed explanation
It is given that \(\begin{array}{l} x+\frac{1}{x}=2 \sin \alpha \Rightarrow x=\sin \alpha+i \cos \alpha=\cos \left(\frac{\pi}{2}-\alpha\right) +i \sin \left(\frac{\pi}{2}-\alpha\right) \\ \Rightarrow \quad x=e^{i\left(\frac{\pi}{2}-\alpha\right)} \end{array}\) and…
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