Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

$\cot \frac{A}{2}\cot \frac{C}{2}=3\Rightarrow \frac{\cos \frac{A}{2}\cos \frac{C}{2}}{\sin \frac{A}{2}\sin \frac{C}{2}}=3\Rightarrow \frac{\cos \frac{A-C}{2}}{\cos \frac{A+C}{2}}=2$ (componendo and dividendo) $\Rightarrow \frac{2\sin \frac{A+C}{2}\cos \frac{A-C}{2}}{2\sin \frac{A+C}{2}\cos \frac{A+C}{2}}=2\Rightarrow \sin A+\sin C=2\sin B$