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solve 1 + cos theta = 2 cos^2 theta

Sagot :

loneguy

[tex]~~~~1+ \cos \theta = 2 \cos^2 \theta \\\\\implies 2\cos^2 \theta -\cos \theta -1 = 0\\\\\implies 2 \cos^2 \theta -2\cos \theta + \cos \theta -1 = 0\\\\\implies 2 \cos \theta( \cos \theta -1) +(\cos \theta -1)=0\\\\\implies (\cos \theta -1)(2 \cos \theta +1)=0\\\\\implies \cos \theta = 1, ~~\cos \theta = -\dfrac 12\\\\\implies \theta = 2n\pi,~~~ \theta = 2n\pi \pm \dfrac{2\pi}3[/tex]

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