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Let's verify the identity $\cos(2\theta)=1-2\sin^2(\theta)$ . What is a good first step?

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

What can we do to simplify our last equation?

A. $2\cos^2(\theta)-2\cos(\theta)+1=0$
B. $\cos^2(\theta)= 1-3\sin^2(\theta)$
C. $2\cos(\theta)= 1-2\sin(\theta)$
D. $\cos^2(\theta)= \csc^2(\theta)-2$
E. $-2\cos^2(\theta)+2\cos(\theta)+1=0$
F. $\cos^2(\theta)+\sin^2(\theta)= 1$
G. None of the above

How can we finish the proof?

A. We know our last equation is true by the definition of cosecant.
B. Divide by $\cos^2(\theta)$ to obtain an equation we know is true.
C. This equation is the square root of the Pythagorean Identity.
D. Our original equation must also be true since it is equivalent to the Pythagorean Identity.
E. We can factor the polynomial to solve for all values of $\theta$ .
F. None of the above