Answer each of the following questions in one word or one sentence or as per exact requirement of the question.
Answer each of the following questions in one word or one sentence or as per exact requirement of the question.
In a $\triangle \mathrm{ABC}$, if $\sin A$ and $\sin B$ are the roots of the equation $c^{2} x^{2}-c(a+b) x+a b=0$, then find $\angle C .$
It is given that $\sin A$ and $\sin B$ are the roots of the equation $c^{2} x^{2}-c(a+b) x+a b=0$.
$\therefore \sin A+\sin B=-\frac{-c(a+b)}{c^{2}} \quad$ (Sum of roots $=-\frac{b}{a}$ )
$\Rightarrow \sin A+\sin B=\frac{a+b}{c}$
$\Rightarrow \sin A+\sin B=\frac{k \sin A+k \sin B}{k \sin C}$ (Sine rule)
$\Rightarrow \sin A+\sin B=\frac{\sin A+\sin B}{\sin C}$
$\Rightarrow \sin C=1=\sin 90^{\circ}$
$\Rightarrow C=90^{\circ}$
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