MHT CET · Maths · Trigonometric Ratios & Identities
If \(3 \sin \alpha=5 \sin \beta\), then \(\tan \left(\frac{\alpha+\beta}{2}\right) \div \tan \left(\frac{\alpha-\beta}{2}\right)=\)
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
\(\frac{\sin \alpha}{\sin \beta}=\frac{5}{3}\) \(\frac{\tan \left(\frac{\alpha+\beta}{2}\right)}{\tan \left(\frac{\alpha-\beta}{2}\right)} = \frac{\sin \alpha+\sin \beta}{\sin \alpha-\sin \beta} = \frac{5+3}{5-3} = \frac{8}{2} = 4\)
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