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

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Simplify cos(2x) first. \[\cos(2x)=\cos^{2}(x)\sin^{2}(x)\] \[=\cos^{2}(x)(1cos^{2}(x))\] \[=\cos^{2}(x)1+\cos^{2}(x)\] \[=2\cos^{2}(x)1\]  \[2\cos^{2}(x)1=\cos(x)\] \[2\cos^{2}(x)\cos(x)1=0\] \[(2\cos(x)+1)(\cos(x)1)=0\] \[\cos(x)=\frac{ 1 }{ 2 }\] or \[\cos(x)=1\] \[x=0, 120, 240, 360 \]
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