Question

sin(B+C) = √3/2
sin(A + C) = sin B and
sin A = 1/2
and
Find sin(A + B - C)​

Answer 1

Answer:

-1/2

Step-by-step explanation:

$\sin( \alpha + \beta ) = \frac{ \sqrt{3} }{2} \\ \alpha + \beta = { \sin - 1} \sin( \frac{\pi}{3} ) \\ \alpha + \beta = \frac{\pi}{3} \\ \sin( \alpha ) = \frac{1}{2} \\ \alpha = \frac{\pi}{6} \\ \beta + \frac{\pi}{3} = \frac{\pi}{6} \\ \beta = - \frac{\pi}{3} \\ \sin( \alpha + c) = \sin( \beta ) \\ \alpha + c = \beta \\ c = - \frac{\pi}{3} - \frac{\pi}{6} \\ c = - \frac{\pi}{2} \\ \sin( \alpha + \beta + c) = \sin( \frac{\pi}{6} - \frac{\pi}{3} - \frac{\pi}{2} ) \\ \sin( \frac{\pi}{6} - \frac{\pi}{3} ) \\ - \sin( \frac{\pi}{3} ) \\ - \frac{1}{2}$