Applying an identity of double-angle cosine: $\cos\left(2\theta\right)=1-2\sin\left(\theta\right)^2$

Factor the polynomial $2-2\sin\left(x\right)^2$ by it's greatest common factor (GCF): $2$

Applying the trigonometric identity: $1-\sin\left(\theta \right)^2 = \cos\left(\theta \right)^2$

Using the sine double-angle identity: $\sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right)$

Simplify the fraction $\frac{2\sin\left(x\right)\cos\left(x\right)}{2\cos\left(x\right)^2}$ by $2$

Simplify the fraction by $\cos\left(x\right)$

Apply the trigonometric identity: $\frac{\sin\left(\theta \right)}{\cos\left(\theta \right)}$$=\tan\left(\theta \right)$