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

asked May 1, 2023 29.3k views

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Answer:

+-pi/3 and pi

Explanation:

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

Squaring both sides:

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

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

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

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

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

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

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

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