Exercise
$\cos^2\left(x\right)-\sin^2\left(x\right)+\sin\left(x\right)=1$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation cos(x)^2-sin(x)^2sin(x)=1. Applying the trigonometric identity: \cos\left(\theta \right)^2-\sin\left(\theta \right)^2 = \cos\left(2\theta \right). Applying an identity of double-angle cosine: \cos\left(2\theta\right)=1-2\sin\left(\theta\right)^2. Move everything to the left hand side of the equation. Subtract the values 1 and -1.
Solve the trigonometric equation cos(x)^2-sin(x)^2sin(x)=1
Final answer to the exercise
$x=0+2\pi n,\:x=\pi+2\pi n,\:x=\frac{1}{6}\pi+2\pi n,\:x=\frac{5}{6}\pi+2\pi n\:,\:\:n\in\Z$