If tan alpha = 2 sin beta sin gamma operatorn | vedclass

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(B) We have,$	an \alpha = 2 \sin \beta \sin \gamma \operatorname{cosec}(\beta + \gamma)$$\Rightarrow 	an \alpha = \frac{2 \sin \beta \sin \gamma}{\s

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$	an \gamma, 	an \alpha, 	an \beta$ are in harmonic progression

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(B) We have,$	an \alpha = 2 \sin \beta \sin \gamma \operatorname{cosec}(\beta + \gamma)$$\Rightarrow 	an \alpha = \frac{2 \sin \beta \sin \gamma}{\sin(\beta + \gamma)}$$\Rightarrow 	an \alpha = \frac{2 \sin \beta \sin \gamma}{\sin \beta \cos \gamma + \cos \beta \sin \gamma}$Dividing numerator and denominator by $\sin \beta \sin \gamma$,we get:$\Rightarrow 	an \alpha = \frac{2}{\cot \gamma + \cot \beta}$This implies that $\cot \beta, \cot \alpha, \cot \gamma$ are in arithmetic progression,which means their reciprocals $	an \beta, 	an \alpha, 	an \gamma$ are in harmonic progression.Alternatively,rearranging the expression:$\Rightarrow \frac{1}{	an \alpha} = \frac{\cot \gamma + \cot \beta}{2}$$\Rightarrow \cot \alpha = \frac{\cot \beta + \cot \gamma}{2}$Thus,$\cot \beta, \cot \alpha, \cot \gamma$ are in arithmetic progression,or $	an \beta, 	an \alpha, 	an \gamma$ are in harmonic progression.

If $\tan \alpha = 2 \sin \beta \sin \gamma \operatorname{cosec}(\beta + \gamma)$,then

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