Question

Sin(240-x)+sin(240+x)

Answer 1

2 sin (480/2) cos( -x) because sinx+siny=2sin(x+y/2) cos (x-y/2)
2 sin (240) cosx
2 sin(270-30) cosx
2 -cos(30) cosx
-2 root (3)/2 cosx
root (3) cosx

Answer 2

sin (A- B) +sin(A+B) = 2 sinAcosB

here A= 240, B= x
sin(240-x) +sin(240+x) = 2 sin240cos X

= 2 sin(270-30) cos X
= 2*(-cos 30) cosx
=- 2*√3/2 cosx
=-√3 cosx