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In $∆ l e ABC, a^{2} \sin 2 C + c^{2} \sin 2 A =$

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$∆$

$2 ∆$

$3 ∆$

$4 ∆$

answer is D.

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Detailed Solution

$a^{2} \sin 2 C + c^{2} \sin 2 A = a^{2} . 2 \sin C \cos C + c^{2} 2 \sin A \cos A = a^{2} \frac{c}{R} \cos C + c^{2} \frac{a}{R} \cos A = \frac{ac}{R} (a \cos C + c \cos A) = \frac{abc}{R} = 4 ∆$

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