Question

Solve the equation cos(x/2)=cos x+1. What are the solutions on the interval 0°

Answer 1

+-pi/3 and pi

Explanation:

`\cos(x/2)=\pm\sqrt{(1+\cos x)/(2)}=\cos x +1`

Squaring both sides:

`(1+\cos x)/(2)=(\cos x + 1)^2`

`(1+\cos x)/(2)=\cos^2x+2\cos x+1`

`1+\cos x=2\cos^2x+4\cos x +2`

`2\cos^2x+3\cos x +1 =0`

`(2\cos x + 1)(\cos x + 1)=0`

`\cos x = -(1)/(2), -1`

`x= \pm(\pi)/(3), \pi`