a2sin2C+c2sin2A=a22sinC⋅cosC+c22sinA⋅cosA=a2⋅CRcosC+c2⋅aRcosA=acR(acosC+ccosA)=abcR=4Δ

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$a^{2} \sin 2 C + c^{2} \sin 2 A =$

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$2 Δ$

$4 Δ$

$3 Δ$

$Δ$

answer is D.

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Detailed Solution

$a^{2} \sin 2 C + c^{2} \sin 2 A = a^{2} 2 \sin C \cdot \cos C + c^{2} 2 \sin A \cdot \cos A$

$= a^{2} \cdot \frac{C}{R} \cos C + c^{2} \cdot \frac{a}{R} \cos A$

$= \frac{a c}{R} (a \cos C + c \cos A)$

$= \frac{a b c}{R} = 4 Δ$

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