simplify sin (π+x) - sin (π-x)
a. -2cos x
b. -2 sin x
c. 2 cos x
d. 2 sin x
sin (pi + x) - sin (pi - x)
[ sin pi * cos x + sin x * cos pi ] - [ sin pi * cos x - sin x * cos pi ] =
2sin x * cos pi =
2sinx * -1
-2sin x
simplify sin (π+x) - sin (π-x)
Because \(\sin(\pi+x) = - \sin(\pi-x)\)
\(\begin{array}{|rcll|} \hline && \sin(\pi+x) - \sin(\pi-x) \\ &=& -\sin(\pi-x) - \sin(\pi-x) \\ &=& -2\cdot \sin(\pi-x) \quad & | \quad \sin(\pi-x) = \sin(x)\\ &=& -2\cdot \sin(x) \\ \hline \end{array}\)