Question

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

Answer 1

Step-by-step explanation:

Answer

Expand the compound angles:

sin x +sin (x+2π/3) +sin (4π/3)

= sin x - 0.5 * sin x + (√3 / 2) * cos x - 0.5 * sin x - (√3 / 2) * cos x

= 0

( cos (2π/3) = -1/2 = cos (4π/3), and

sin (2π/3) = √3 / 2 = -sin (4π/3)

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