use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine cos^4 2x

iam confused about the first part so can someone just show me hoe to do the beginning and then i will continue

\[ \cos^2(x)= \frac 1 2 ( 1+ \cos(2x)) \]

\[ \cos^4(x)= \frac 1 4 (1+\cos(2x))^2 \]

ok after that what do i do to change ^^ into co^4 2x

\[ (\cos (2 x)+1)^2=\cos ^2(2 x)+2 \cos (2 x)+1 \]

\[ \cos^2(2 x) = \frac 1 2( 1 + \cos(4x)) \]

Putting them together, you get \[\cos ^4(x)=\frac{1}{8} (4 \cos (2 x)+\cos (4 x)+3) \]

Did you get it?

but iam looking for cos^4 2x

not cos^4 x

Replace every x by 2x in the answer and you will get \[ \cos ^4(2 x)=\frac{1}{8} (4 \cos (4 x)+\cos (8 x)+3) \]

thanku so much

yw

by the way if i close this question and i want to check it again can it or will it be deleted by tomorrow?

No it will not be deleted.

so i could check at any time in the closed questions section

I think so.

ok thanks again

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