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Circular Measurement of Angle

In ABC,b2si...

Question

In $△ A B C, b^{2} sin 2 C + c^{2} sin 2 B$ =

Δ

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2 Δ

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4 Δ

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Δ / 2

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Solution

The correct option is C $4 Δ$
$b^{2} sin 2 c + c^{2} sin 2 B$
$b^{2} (2 sin c cos c) + c^{2} (2 sin B \cdot cos B)$
$2 b (b sin c) cos c + 2 c (c sin B) \cdot cos B$
$2 b (c sin B) \cdot cos c + 2 c (b sin c) cos B$
$2 b c (sin B cos c + sin c cos B)$
$2 b c (sin B + c)$
$2 b c (sin 180 - A)$
$2 b c sin A$
$= 2 \times 2 \times \frac{1}{2} b c sin A$
$= 4 \times \frac{1}{2} b c sin A$
$= 4 ($ area of $D^{4})$ .

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