Exercise
$\cos^2\left(2x\right)+\sin^2\left(x\right)\cos\left(x\right)=1$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation cos(2x)^2+sin(x)^2cos(x)=1. Move everything to the left hand side of the equation. Apply the trigonometric identity: -1+\cos\left(\theta \right)^2=-\sin\left(\theta \right)^2, where x=2x. Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right). The power of a product is equal to the product of it's factors raised to the same power.
Solve the trigonometric equation cos(2x)^2+sin(x)^2cos(x)=1
Final answer to the exercise
$x=0+2\pi n,\:x=\pi+2\pi n,\:x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n\:,\:\:n\in\Z$