Exercise
$\sin\left(x\right)\sin\left(2x\right)+2\:\left(\sin\left(x\right)^2\right)$
Step-by-step Solution
Learn how to solve differential equations problems step by step online. Simplify the trigonometric expression sin(x)sin(2x)+2sin(x)^2. Factor the polynomial \sin\left(x\right)\sin\left(2x\right)+2\sin\left(x\right)^2 by it's greatest common factor (GCF): \sin\left(x\right). Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right). Factor the polynomial \left(2\sin\left(x\right)\cos\left(x\right)+2\sin\left(x\right)\right) by it's greatest common factor (GCF): 2\sin\left(x\right). Applying the trigonometric identity: \sin\left(\theta \right)^2 = 1-\cos\left(\theta \right)^2.
Simplify the trigonometric expression sin(x)sin(2x)+2sin(x)^2
Final answer to the exercise
$2-2\cos\left(x\right)^2+2\cos\left(x\right)-2\cos\left(x\right)^{3}$