Answer
$$\cos 2A =1-2\sin^2A$$
Work Step by Step
Since
\begin{align*}
\cos 2A&=\cos^2A-\sin^2A,\ \ \ \ \ \ \ \ \ \text{Use }\cos^2x+\sin^2x=1 \\
&=(1-\sin^2A)-\sin^2A\\
&=1-2\sin^2A
\end{align*}
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