Using the trig identity $\displaystyle \sin^2 \theta + \cos^2 \theta = 1$
Then: $\displaystyle \sqrt{1-\sin^2 \theta} = \sqrt{\cos^2 \theta} = \cos \theta$
Since there is a $\displaystyle \cos \theta$ on both the denominator and numerator, they cancel out.
Then by using power reducing formulas:
$\displaystyle \sin^2 \theta = \dfrac{1-\cos(2\theta)}{2}$
$\displaystyle \sin^2 \theta = \frac{1-cos 2\theta}{2}$ is the standard power reducing formula which is worth memorizing for a calculus class since it is used so often.
You can derive it by writing $\displaystyle \cos 2\theta$ in terms of $\displaystyle \sin^2 \theta$ and solving for $\displaystyle \sin^2 \theta$.