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