Question

If cosx+2cos(x+240°)=1

Determine the general equations

Answer 1

Cos(x) + cos (x+240^o) =1

$\implies$

$cos(x)+cos(x+{24\pi \over18}) = 1$

$cos(x)+cos(x+{24\pi \over18}) = cos(0)$

We know that $\boxed{cos(a+b) = cos(a)cos(b)-sin(a)sin(b)}$

$\implies$

$\boxed{cos(x)+cos(x)cos(24\pi/18)-sin(x)sin(24\pi/18)=cos(0)}$

On solving this

We got

$\boxed{x = \frac{1}{3}(6\pi n +\pi)}$