Prove that cos x + cos (120 0 – x) + cos (120 0 + x) = 0

Question

Philoid · Accepted Answer

In this question the following formulas will be used:

cos (A + B) = cosAcosB – sinAsinB

cos (A - B) = cosAcosB+ sinAsinB

= cos x + cos 120⁰ cosx – sin120sinx + cos 120⁰cosx+sin120sinx

= cosx + 2cos120 cosx

=cosx + 2cos (90 + 30) cosx

= cosx + 2 (-sin30) cosx

=cosx - 2 cosx

=

=0.

Prove thatcos x + cos (1200 – x) + cos (1200 + x) = 0