Problem

Expand cos2⁡x using double-angle formulas.

Answer

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Answer

We need to express cos2⁡x in terms of cos⁡2x, so we rearrange the second double-angle formula to solve for cos2⁡x: cos2⁡x=cos⁡2x+12

Steps

Step 1 ：First, recall the double-angle formula for cosine: cos⁡2x=1−2sin2⁡x or cos⁡2x=2cos2⁡x−1.

Step 2 ：We need to express cos2⁡x in terms of cos⁡2x, so we rearrange the second double-angle formula to solve for cos2⁡x: cos2⁡x=cos⁡2x+12

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