TS EAMCET · Maths · Trigonometric Ratios & Identities
If \(3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)\) and \(\alpha+\beta \neq \frac{\pi}{2}\), then \(\frac{\tan \left(\frac{\pi}{4}-\alpha\right)}{\tan \left(\frac{\pi}{4}-\beta\right)}=\)
- A \(0\)
- B \(-4\)
- C \(-\frac{1}{4}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(C) \(-\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\(3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)\) \(3(\sin\alpha \cos\beta - \cos\alpha \sin\beta) = 5(\cos\alpha \cos\beta - \sin\alpha \sin\beta)\) \(3(\tan\alpha - \tan\beta) = 5(1 - \tan\alpha \tan\beta)\) \(3\tan\alpha - 3\tan\beta = 5 - 5\tan\alpha \tan\beta\)…
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