Question

Simplify the expression

sin(pi+x) + sin(pi - x)

Answer 1

sin(x+ip)+sin(-x+ip)

Answer 2

is it?

Answer 3

NO , the answer is zero

Answer 4

\[\sin(x+\pi)=\sin(x)\cos(\pi)+\sin(\pi)\cos(x)=\sin(x)(-1)+0\cos(x)=-\sin(x)\]
\[\sin(\pi-x)=\sin(\pi)\cos(x)-\sin(x)\cos(\pi)=0\cos(x)-\sin(x)(-1)=\sin(x)\]

Answer 5

what is -sin(x)+sin(x)
?

Answer 6

of course you don't have to do all this but you can

Answer 7

sine is periodic with period
\[2\pi\] and
\[x+\pi\]
\[-x+\pi\] are
\[2\pi\] units apart. therefore the function is the same at both those points, and so the difference is zero

Answer 8

sorryy :(

Answer 9

yes its -sin(x)+sin(x)