Exercise
$1+\sin\left(2x\right)=\sin\left(x\right)^2$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation 1+sin(2x)=sin(x)^2. Grouping all terms to the left side of the equation. Applying the trigonometric identity: 1-\sin\left(\theta \right)^2 = \cos\left(\theta \right)^2. Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right). Factor the polynomial \cos\left(x\right)^2+2\sin\left(x\right)\cos\left(x\right) by it's greatest common factor (GCF): \cos\left(x\right).
Solve the trigonometric equation 1+sin(2x)=sin(x)^2
Final answer to the exercise
$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n,\:x=0\:,\:\:n\in\Z$