Question

prove that cos theta +
(2π/3+theta) + cos (4π/3+theta) = 0​

Answer 1

Answer:

0

Step-by-step explanation:

Let xcosθ=ycosθ+2π3=zcosθ+4π3=k

Now,

kx=cosθ.....1

ky=cosθ+2π3......2

kz=cosθ+4π3......3

By adding 1,2,and3 we get

kx+ky+kz=cosθ+cosθ+2π3+cosθ+4π3

⇒k1x+1y+1z=cosθ+cosθ+2π3+cosθ+4π3

=2cos2θ+4π32cos-4π32+cosθ+2π3[∵cosA+cosB=2cosA+B2cosA-B2]

=-2cosθ+2π3cos2π3+cosθ+2π3

=-2×12cosθ+2π3+cosθ+2π3bycos2π3=12

=0