Exercise
$2\left(cos^2\left(x\right)-sen^2\left(x\right)\right)=1$
Step-by-step Solution
Learn how to solve multiply powers of same base problems step by step online. Solve the trigonometric equation 2(cos(x)^2-sin(x)^2)=1. Applying the trigonometric identity: \cos\left(\theta \right)^2-\sin\left(\theta \right)^2 = \cos\left(2\theta \right). Applying an identity of double-angle cosine: \cos\left(2\theta\right)=1-2\sin\left(\theta\right)^2. Solve the product 2\left(1-2\sin\left(x\right)^2\right). We need to isolate the dependent variable x, we can do that by simultaneously subtracting 2 from both sides of the equation.
Solve the trigonometric equation 2(cos(x)^2-sin(x)^2)=1
Final answer to the exercise
$x=\frac{1}{6}\pi+2\pi n,\:x=\frac{5}{6}\pi+2\pi n\:,\:\:n\in\Z$