If $\alpha ,\beta$ are solutions of $a\cos x+b\sin x=c$  then $\sin \alpha +\sin \beta =$

$\begin{array}{l}a\cos x+b\sin x=c\\ a\cos x=c-b\sin x\\ a^2{\cos }^{2}x=c^2+b^2{\sin }^{2}x-2bc.\sin x\\ (a^2+b^2){\sin }^{2}x-2bc.\sin x+(c^2-a^2)=0\to \left(1\right)\\ \sin \alpha .\sin \beta \text{ are the roots of eq.shion }\left(1\right)\\ \Rightarrow \sin \alpha +\sin \beta =\frac{2bc}{a^2+b^2}\end{array}$