Solve the trigonometric equation cos(x)^2=cos(2x)

 Exercise

$cos^2\left(x\right)=cos\left(2x\right)$

 

Grouping all terms to the left side of the equation

$\cos\left(x\right)^2-\cos\left(2x\right)=0$

 

Simplify $\cos\left(x\right)^2-\cos\left(2x\right)$ by applying trigonometric identities

$\sin\left(x\right)^2=0$

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Removing the variable's exponent raising both sides of the equation to the power of $\frac{1}{2}$

$\sin\left(x\right)=0$

 

The angles where the function $\sin\left(x\right)$ is $0$ are

$x=0^{\circ}+360^{\circ}n,\:x=180^{\circ}+360^{\circ}n$

 

The angles expressed in radians in the same order are equal to

$x=0+2\pi n,\:x=\pi+2\pi n\:,\:\:n\in\Z$

$x=0+2\pi n,\:x=\pi+2\pi n\:,\:\:n\in\Z$

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