Question

In the $\Delta ABC$ ,if $\frac{\sin A}{c\sin B}+\frac{\sin B}{c}+\frac{\sin C}{b}=\frac{c}{ab}+\frac{b}{ac}+\frac{a}{bc}$.then the value of angle A is?

• A. ${120}^{\circ }$
• B. ${90}^{\circ }$
• C. ${60}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

Answer: (B)

${90}^{\circ }$

From Sin law $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$
$\frac{\sin A}{c\sin B}+\frac{\sin B}{c}+\frac{\sin C}{b}=\frac{c}{ab}+\frac{b}{ac}+\frac{a}{bc}$
$\Rightarrow \frac{a\sin A}{cb\sin A}+\frac{b\sin A}{ac}+\frac{c\sin A}{ab}=\frac{c}{ab}+\frac{b}{ac}+\frac{a}{bc}$
Only when $\sin A=1\Rightarrow A=90^0$