Problem involving Power-Reducing Formula

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The discussion revolves around a problem involving a power-reducing formula in trigonometry. A participant is confused about how a solution arrived at the value of 27/8. They attempted to solve the problem by first simplifying the fractions before distributing a factor of 9, resulting in a different expression than the provided solution. The key point of contention is the arithmetic leading to the 27/8 value, specifically the addition of fractions. Clarification on the steps leading to this result is sought to resolve the discrepancy.
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Homework Statement


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Homework Equations


How in the world did they get their solution? Where did 27/8 come from?


The Attempt at a Solution


I did the arithmetic with the fractions inside before distributing the 9, and ended up getting something like -9/4 cos2x + 9/4 cos4x. Completely different from theirs.
 
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In the step above that, you have 1/4 + 1/8 = 2/8 + 1/8 = 3/8, then times 9 is 27/8
 

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