Exercise
$cos3xcosx-3sin3xsinx$
Step-by-step Solution
Learn how to solve integrals with radicals problems step by step online. Simplify the trigonometric expression cos(3x)cos(x)-3sin(3x)sin(x). Apply the rule of the product of two cosines \cos\left(a\right)\cdot\cos\left(b\right)=\frac{\cos\left(a+b\right)+\cos\left(a-b\right)}{2}. Combining like terms 3x and x. Combining like terms 3x and -x. Apply the trigonometric identity: \sin\left(a\right)\sin\left(b\right)=\frac{\cos\left(a-b\right)-\cos\left(a+b\right)}{2}, where a=3x and b=x.
Simplify the trigonometric expression cos(3x)cos(x)-3sin(3x)sin(x)
Final answer to the exercise
$\frac{\cos\left(4x\right)+\cos\left(2x\right)-3\left(\cos\left(2x\right)-\cos\left(4x\right)\right)}{2}$