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AP EAMCET · Maths · Properties of Triangles

In any \(\triangle A B C, b^2 \sin 2 C+c^2 \sin B\) is equal to

  1. A \(\Delta\)
  2. B \(2 \Delta\)
  3. C \(3 \Delta\)
  4. D \(4 \Delta\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(4 \Delta\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & b^2 \sin 2 C+c^2 \sin 2 B \\ & =2 b^2 \sin C \cos C+2 c^2 \sin B \cos B \\ & =\frac{2 b^2 c \cos C}{2 R}+\frac{2 c^2 b \cos B}{2 R} \\ & \qquad\left[\because \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2 R\right] \\ & =\frac{b c}{R}(b \cos C+c \cos…