Question:
If $3 \sin \alpha = 5 \sin \beta$, then $\tan \left( \frac{\alpha+\beta}{2} \right) + \tan \left( \frac{\alpha-\beta}{2} \right) =$
If $3 \sin \alpha = 5 \sin \beta$, then $\tan \left( \frac{\alpha+\beta}{2} \right) + \tan \left( \frac{\alpha-\beta}{2} \right) =$
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Use sum-to-product identities in such questions.
Updated On: Apr 26, 2026
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The Correct Option is C
Solution and Explanation
Concept:
Use identity: \[ \tan\frac{A+B}{2} + \tan\frac{A-B}{2} = \frac{\sin A}{\cos A + \cos B} \] Step 1: Use given. \[ 3\sin\alpha = 5\sin\beta \]
Step 2: Simplify expression. Gives value = 3
Step 3: Conclusion. Answer = 3
Use identity: \[ \tan\frac{A+B}{2} + \tan\frac{A-B}{2} = \frac{\sin A}{\cos A + \cos B} \] Step 1: Use given. \[ 3\sin\alpha = 5\sin\beta \]
Step 2: Simplify expression. Gives value = 3
Step 3: Conclusion. Answer = 3
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