Exercise
$\cos^2\left(x\right)=\sin^2\left(x\right)\cdot\cos^2\left(x\right)+\cos^5\left(x\right)$
Step-by-step Solution
Learn how to solve polynomial factorization problems step by step online. Solve the trigonometric equation cos(x)^2=sin(x)^2cos(x)^2+cos(x)^5. Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side. Factor the polynomial \cos\left(x\right)^2-\sin\left(x\right)^2\cos\left(x\right)^2-\cos\left(x\right)^5 by it's greatest common factor (GCF): \cos\left(x\right)^2. Applying the trigonometric identity: 1-\sin\left(\theta \right)^2 = \cos\left(\theta \right)^2. Break the equation in 2 factors and set each factor equal to zero, to obtain simpler equations.
Solve the trigonometric equation cos(x)^2=sin(x)^2cos(x)^2+cos(x)^5
Final answer to the exercise
$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n,\:x=0,\:x=0\:,\:\:n\in\Z$