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Answer:
C. 2cos²(x)
Explanation:
The relevant identities are ...
cos(2x) = cos²(x) -sin²(x)
cos²(x) = 1 -sin²(x)
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Then the expression can be simplified to ...
cos(2x) +1 = (cos²(x) -sin²(x)) +1 = cos²(x) +(1 -sin²(x)) = cos²(x) +cos²(x)
= 2cos²(x)