<s>[INST] solving for sin of the sum of two angles of a triangle In triangle $ABC$, 
$3\sin B+4\cos C=6$ and $4\sin C+3\cos B=1$. 
Show that $\sin(B+C)=0.5$.
Can we assume $\angle A = 180 - ( B + C)$ and use sum formula.
 [/INST] Squaring both equations yields: 
$9\sin^2 B + 24 \sin B\cos C + 16 \cos^2 C = 36$
$9\cos^2 B + 24 \cos B\sin C + 16 \sin^2 C = 1$
Now what happens when you add the two together?
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