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simplify sin (π+x) - sin (π-x)

a. -2cos x

b. -2 sin x

c. 2 cos x

d. 2 sin x

nlbradshaw0430  Apr 13, 2017
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2+0 Answers

 #1
avatar+79741 
+2

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

 

 

cool cool cool

CPhill  Apr 13, 2017
 #2
avatar+18777 
+2

simplify sin (π+x) - sin (π-x)

 

Because \(\sin(\pi+x) = - \sin(\pi-x)\)

 

\(\begin{array}{|rcll|} \hline && \sin(\pi+x) - \sin(\pi-x) \\ &=& -\sin(\pi-x) - \sin(\pi-x) \\ &=& -2\cdot \sin(\pi-x) \quad & | \quad \sin(\pi-x) = \sin(x)\\ &=& -2\cdot \sin(x) \\ \hline \end{array}\)

 

laugh

heureka  Apr 13, 2017
edited by heureka  Apr 13, 2017

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