Answer to Question #185418 in Trigonometry for Thabisile

Question #185418

Cosx+2cos(x+240°)

Simplify the equation


1
Expert's answer
2021-05-11T09:19:36-0400

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

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

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

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

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


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

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