SOLUTION: Use the power-reducing formulas to rewrite each of the expressions in terms of the first power of the cosine. sin^4 2x

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Question 1177495: Use the power-reducing formulas to rewrite each of the expressions in terms of the first power of the cosine. sin^4 2x
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.

sin(2x) = 2sin(x)*cos(x).


THEREFORE,  sin^4(2x) = (2sin(x)*cos(x))^4 = 16cos^4(x)*(1-cos^2(x))^2 = 16cos^4(x)*(1-2cos^2(x) + cos^4(x)).


It is the formula you are looking for.



If necessary, you can apply FOIL to the last expression.