Question

If cos x+ cosy + cos z = 0 then find the value of cos 3x + cos 3y + cos 3z​

Answer 1

Answer:

cos z = -(cos x + cos y)

and similar for sin z.

Square both equations and add to get

1=2+2(cos x cos y + sin x sin y)

cos(y-x)=-1/2.

y-x= \pm 2\pi/3 + 2n\pi.

Suppose y-x=2\pi/3+2n\pi.

cos y = cos(x+2\pi/3) =-1/2cos x - r3/2sin x,

sin y = sin (x+2\pi/3) = -1/2sin x+r3/2cos x.

cos z = -(cos x - 1/2cos x - r3/2sin x)

=-cos(x+\pi/3)

=cos(x-2\pi/3).

sin z=-(sin x - 1/2sinx + r3/2cos x)

=-sin(x+\pi/3)

=sin(x-2\pi/3).

So z=x-2\pi/3.

cos 3x+cos3y+cos 3z

=cos 3x +cos3x+cos3x

=3cos3x

=3cos(x+y+z).

Step-by-step explanation: