Trigonometric Value: Cosine Double Angle
The question asks for the value of $\cos 2A$ given the condition $\cos A = 1 - 2\sin^2A$.
We need to recall the standard trigonometric identities for the double angle of cosine ($\cos 2A$). The common forms are:
- $\cos 2A = \cos^2 A - \sin^2 A$
- $\cos 2A = 2\cos^2 A - 1$
- $\cos 2A = 1 - 2\sin^2 A$
Observe that one of the standard identities for $\cos 2A$ is $\cos 2A = 1 - 2\sin^2 A$. This expression matches Option 2.
The condition given, $\cos A = 1 - 2\sin^2A$, means that for the specific angle $A$ considered, the value of $\cos A$ is equal to the expression $1 - 2\sin^2A$. Since $\cos 2A$ is identically equal to $1 - 2\sin^2A$, the value of $\cos 2A$ is represented by this expression.
Therefore, based on the standard trigonometric identity, the value of $\cos 2A$ is $1 - 2\sin^2A$.
Final Answer: The final answer is $\boxed{1 - 2\sin^2A}$
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