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  4. If 3 sin α=5 sin β, then ( tan (α+β/2)/ tan (α-β)2) is equal to

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Q. If $3 \sin \alpha=5 \sin \beta$, then $\frac{\tan \frac{\alpha+\beta}{2}}{\tan \frac{\alpha-\beta}{2}}$ is equal to

Trigonometric Functions

Solution:

$\because 3 \sin \alpha=5 \sin \beta$
$\Rightarrow \frac{\sin \alpha}{\sin \beta}=\frac{5}{3} $
$\Rightarrow \frac{\sin \alpha+\sin \beta}{\sin \alpha-\sin \beta}=\frac{8}{2} $
$\Rightarrow \frac{\tan \left(\frac{\alpha+\beta}{2}\right)}{\tan \left(\frac{\alpha-\beta}{2}\right)}=4$