20. Expressed as a single trigonometric function, $\cos ^{2}(6 m)-\sin ^{2}(6 m)$ is equal to:
$2 \cos (3 m)$
$1-2 \cos (3 m)$
$\cos (12 m)$
$\sin (12 m)$

Answer

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Answer

Final Answer: The equivalent single trigonometric function for $\cos ^{2}(6 m)-\sin ^{2}(6 m)$ is $\boxed{\cos (12 m)}$.

Steps

Step 1 ：The given expression is in the form of $\cos^2(x) - \sin^2(x)$ which is equivalent to $\cos(2x)$.

Step 2 ：So, we can replace $x$ with $6m$ to get the equivalent single trigonometric function.

Step 3 ：Final Answer: The equivalent single trigonometric function for $\cos ^{2}(6 m)-\sin ^{2}(6 m)$ is $\boxed{\cos (12 m)}$.