Question

Cos (x + π/ 3) + cos (x - π/ 3) = 1 Solve for "x" on the interval [0, 2pi)

Answer 1

$\bf cos\left( x+\frac{\pi }{3} \right)+cos\left( x-\frac{\pi }{3} \right)=1\\\\ -----------------------------\\\\\ [cos(x)cos\left( \frac{\pi }{3} \right)\underline{-sin(x)sin\left( \frac{\pi }{3} \right)}] + [cos(x)cos\left( \frac{\pi }{3} \right)\underline{+sin(x)sin\left( \frac{\pi }{3} \right)}]=1$

$\bf cos(x)cos\left( \frac{\pi }{3} \right)+cos(x)cos\left( \frac{\pi }{3} \right)=1\implies 2cos(x)cos\left( \frac{\pi }{3} \right)=1 \\\\\\ 2cos(x)\cdot \cfrac{1}{2}=1\implies cos(x)=1\implies \measuredangle x=cos^{-1}(1) \\\\\\ \measuredangle x = \begin{cases} 0\\ 2\pi \end{cases}$