Exercise
$\frac{\left(1+cos\left(z\right)\left(1-cos\left(z\right)\right)\right)}{tan^2\left(z\right)}=cos^2$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation (1+cos(z)(1-cos(z)))/(tan(z)^2)=cos(z)^2. Multiply both sides of the equation by \tan\left(z\right)^2. Simplify \cos\left(z\right)^2\tan\left(z\right)^2 into \sin\left(z\right)^2 by applying trigonometric identities. Multiply the single term \cos\left(z\right) by each term of the polynomial \left(1-\cos\left(z\right)\right). Apply the trigonometric identity: 1-\cos\left(\theta \right)^2=\sin\left(\theta \right)^2, where x=z.
Solve the trigonometric equation (1+cos(z)(1-cos(z)))/(tan(z)^2)=cos(z)^2
Final answer to the exercise
$z=\frac{1}{2}\pi+2\pi n,\:z=\frac{3}{2}\pi+2\pi n\:,\:\:n\in\Z$