Question

In $\Delta ABC,\frac{1}{2}{a}^2\frac{sinBsinC}{sinA}=$

• A. $\Delta$
• B. $2\Delta$
• C. $3\Delta$
• D. $4\Delta$

Answer 1

The correct option is A $\Delta$

In $△ABC$

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}⟹\frac{\sin B}{\sin A}=\frac{b}{a}$

$\therefore \frac{1}{2}{a}^2\frac{\sin B\sin C}{\sin A}=\frac{1}{2}{a}^2\times \frac{\sin B}{\sin A}\times \sin C=\frac{1}{2}{a}^2\times \frac{b}{a}\times \sin C=\frac{1}{2}ab\sin C=\Delta$