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abbyl94

  • 3 years ago

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

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  1. Azteck
    • 3 years ago
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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 \[\cos(x)=1\] \[x=0, 120, 240, 360 \]

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