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AM,GM,HM Inequality

In a ABC sh...

Question

In a $△ A B C$ show that $2 r^{2} sin A sin B sin C = △$ .

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Solution

Mistake : $R$ must be there instead of $r$
In $△ A B C, Δ = \frac{a b c}{4 R} = \frac{(2 R sin A) (2 R sin B) (2 R sin C)}{4 R} = 2 R^{2} sin A sin B sin C$
$R H S = L H S$
Hence Proved

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