Question

cosθ+cos(120°+θ)+cos(120°−θ)=​

Answer 1

Answer:

Others have answered this question algebraically. For a change, let’s answer it geometrically.

Obtain an equilateral triangle whose sides are of length 1 unit.

Position this triangle in a vertical plane so that one of the sides is θ° from the vertical.

Observe that the other sides are (120+θ)° and (120–θ)° from the vertical.

Imagine an ant crawling around the equilateral triangle.

As it crawls along the first side, its altitude increases by cosθ.

As it crawls along the second side, its altitude increases by cos(120+θ).

As it crawls along the third side, its altitude increases by cos(120-θ).

But, it is then back where it started, so its total increase in altitude is 0.

So cosθ+cos(120°+θ)+cos(120°–θ) = 0

Answer 2

ANSWER

0

STEP BY STEP EXPLANATION

cos(x+y)+cos(x−y)=2cosxcosy    

cosθ+[cos(120°+θ)+cos(120°−θ)]

=cosθ+2cos120°cosθ

=cosθ+2(−1/2)cosθ

=cosθ−cosθ

=0

HOPE IT HELPED !!!!