How do you solve the equation $cos 2 x (2 cos x + 1) = 0$ $cos2x(2cosx+1)=0$ ?

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How do you solve the equation $cos 2 x (2 cos x + 1) = 0$ $cos2x(2cosx+1)=0$ ?

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Answer 1 · 2017-02-22T09:11:01

Solution is $x = (2 n + 1) \frac{π}{4}$ $x=(2n+1)pi/4$ or $x = 2 n π \pm \frac{2 π}{3}$ $x=2npi+-(2pi)/3$ , where $n$ $n$ is an integer

Explanation:

As $cos 2 x (2 cos x + 1) = 0$ $cos2x(2cosx+1)=0$ , we have

either $cos 2 x = 0$ $cos2x=0$ i.e. $2 x = (2 n + 1) \frac{π}{2}$ $2x=(2n+1)pi/2$ , where $n$ $n$ is an integer and $x = (2 n + 1) \frac{π}{4}$ $x=(2n+1)pi/4$

or $2 cos x + 1 = 0$ $2cosx+1=0$ i.e. $cos x = - \frac{1}{2} = cos (\pm \frac{2 π}{3})$ $cosx=-1/2=cos(+-(2pi)/3)$ and $x = 2 n π \pm \frac{2 π}{3}$ $x=2npi+-(2pi)/3$ , where $n$ $n$ is an integer

Hence, solution is $x = (2 n + 1) \frac{π}{4}$ $x=(2n+1)pi/4$ or $x = 2 n π \pm \frac{2 π}{3}$ $x=2npi+-(2pi)/3$ , where $n$ $n$ is an integer

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How do you solve the equation $cos 2 x (2 cos x + 1) = 0$ $cos2x(2cosx+1)=0$ ?

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How do you solve the equation $cos 2 x (2 cos x + 1) = 0$ $cos2x(2cosx+1)=0$ ?