Final Answer
$x=\frac{1}{6}\pi+\pi n,\:x=\frac{5}{6}\pi+\pi n\:,\:\:n\in\Z$
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Step-by-step Solution
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1
Applying the trigonometric identity: $\cos\left(\theta \right)^2-\sin\left(\theta \right)^2 = \cos\left(2\theta \right)$
$\cos\left(2x\right)=\frac{1}{2}$
Why is cos(2x) = cos(x)^2 - sin(x)^2 ?
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$\cos\left(2x\right)=\frac{1}{2}$
Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation cos(x)^2-sin(x)^2=1/2. Applying the trigonometric identity: \cos\left(\theta \right)^2-\sin\left(\theta \right)^2 = \cos\left(2\theta \right). The angles where the function \cos\left(2x\right) is \frac{1}{2} are. Solve the equation (1). Divide both sides of the equation by 2.
Final Answer
$x=\frac{1}{6}\pi+\pi n,\:x=\frac{5}{6}\pi+\pi n\:,\:\:n\in\Z$