Question

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

Answer 1

Answer:

+-pi/3 and pi

Step-by-step explanation:

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

Squaring both sides:

$\dfrac{1+\cos x}{2}=(\cos x + 1)^2$

$\dfrac{1+\cos x}{2}=\cos^2x+2\cos x+1$

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

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

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

$\cos x = -\dfrac{1}{2}, -1$

$x= \pm\dfrac{\pi}{3}, \pi$