Let's verify the identity $\sin(2\theta)=\frac{2\tan(\theta)}{\sec^2(\theta)}$. What happens when we rewrite the right-hand side using only sine and cosine?

A. $\sin(2\theta)=\frac{2\frac{\sin(\theta)}{\cos(\theta)}}{\frac{1}{\cos^2(\theta)}}$
B. $\sin(2\theta)=2\frac{\cos^2(\theta)}{\sin(\theta)}$
C. $\sin(2\theta)=2\frac{\sin^2(\theta)}{\cos(\theta)}$
D. $\sin(2\theta)=\frac{2\frac{\sin(\theta)}{\cos(\theta)}}{\frac{1}{\sin^2(\theta)}}$
E. None of the above

How can we simplify the right-hand side?

A. $\sin(2\theta)=2\frac{\sin(\theta)}{\cos(\theta)}$
B. $\sin(2\theta)=2\frac{1-\sin^2(\theta)}{\sin(\theta)}$
C. $\sin(2\theta)=2\frac{1-\cos^2(\theta)}{\cos(\theta)}$
D. $\sin(2\theta)=2\frac{\sin^3(\theta)}{\cos(\theta)}$
E. $\sin(2\theta)=\cos^2(\theta)-\sin^2(\theta)$
F. $\sin(2\theta)=2\sin(\theta)\cos(\theta)$
G. None of the above

How can we finish the proof?

A. The previous equation is just the double angle formula for sine.
B. The previous equation is just the double angle formula for cosine.
C. Multiply by $\sin(\theta)$ on both sides to then solve for all values of $\theta$.
D. Apply the Pythagorean Identity to get that the left and right hand sides are equal.
E. None of the above