Exercise
$cos\:\left(3x\right)cos\left(x\right)-\sin\left(3x\right)\cdot\sin\left(x\right)=1$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation cos(3x)cos(x)-sin(3x)sin(x)=1. Using the cosine of a sum formula: \cos(\alpha\pm\beta)=\cos(\alpha)\cos(\beta)\mp\sin(\alpha)\sin(\beta), where angle \alpha equals 3x, and angle \beta equals x. Combining like terms 3x and x. The angles where the function \cos\left(4x\right) is 1 are. Solve the equation (1).
Solve the trigonometric equation cos(3x)cos(x)-sin(3x)sin(x)=1
Final answer to the exercise
$x=0+2\pi n,\:x=\frac{1}{2}\pi+\frac{1}{2}\pi n\:,\:\:n\in\Z$