Answer to Question #185418 in Trigonometry for Thabisile

Question

Cosx+2cos(x+240°)

Simplify the equation

Answer 1

cosx + 2cos(x+240$\degree$) = cosx + 2(cosx * cos240$\degree$ - sinx * sin240$\degree$)

= cosx + 2(cosx * (-1/2) - sinx * (- $\sqrt{\smash[b]{3}}$/2))

= cosx + 2(-cosx/2 + $\sqrt{\smash[b]{3}}$sinx/2)

= cosx - cosx + $\sqrt{\smash[b]{3}}$sinx

= $\sqrt{\smash[b]{3}}$sinx

$\therefore$ cosx + 2cos(x+240$\degree$) = $\sqrt{\smash[b]{3}}$sinx