Question

Prove that sinx+sin(x+2π/3)+sin(x+4π/3)=0

Answer 1

here is ur answer..........

Answer 2

Answer:

Step-by-step explanation:

for given term

L.H.S.

$\sin x +\sin (x+\frac{2\Pi }{3})+\sin (x+\frac{4\Pi }{3})\\\\=\sin x +\sin (x+\Pi -\frac{\Pi }{3})+\sin (x+\Pi +\frac{\Pi }{3})\\\\=\sin x -\sin (x-\frac{\Pi }{3})-\sin (x+\frac{\Pi }{3})\\\\=\sin x-[\sin x\cos \frac{\Pi }{3}-\cos x\sin \frac{\Pi }{3}]-[sin x\cos \frac{\Pi }{3}+\cos x\sin \frac{\Pi }{3}\\\\=\sin x-\frac{1}{2}\sin x+\frac{\sqrt{3}}{2}\cos x-\frac{1}{2}\sin x-\frac{\sqrt{3}}{2}\cos x\\\\=\sin x-2*\frac{1}{2}\sin x\\\\=\sin x-\sin x\\\\=0$

as L.H.S. =R.H.S.

hence proved.