## abbyl94 2 years ago cos^2x = cos x solve each equation for principal values of x. express solutions in degrees

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Simplify cos(2x) first. $\cos(2x)=\cos^{2}(x)-\sin^{2}(x)$ $=\cos^{2}(x)-(1-cos^{2}(x))$ $=\cos^{2}(x)-1+\cos^{2}(x)$ $=2\cos^{2}(x)-1$ -------------------------------------------------------- $2\cos^{2}(x)-1=\cos(x)$ $2\cos^{2}(x)-\cos(x)-1=0$ $(2\cos(x)+1)(\cos(x)-1)=0$ $\cos(x)=-\frac{ 1 }{ 2 }$ or $\cos(x)=1$ $x=0, 120, 240, 360$