Answer:
+-pi/3 and pi
Step-by-step explanation:
[tex]\cos(x/2)=\pm\sqrt{\dfrac{1+\cos x}{2}}=\cos x +1[/tex]
Squaring both sides:
[tex]\dfrac{1+\cos x}{2}=(\cos x + 1)^2[/tex]
[tex]\dfrac{1+\cos x}{2}=\cos^2x+2\cos x+1[/tex]
[tex]1+\cos x=2\cos^2x+4\cos x +2[/tex]
[tex]2\cos^2x+3\cos x +1 =0[/tex]
[tex](2\cos x + 1)(\cos x + 1)=0[/tex]
[tex]\cos x = -\dfrac{1}{2}, -1[/tex]
[tex]x= \pm\dfrac{\pi}{3}, \pi[/tex]
