use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine

cos^4 2x

Question

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

nali · Answer

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

anonymous · Answer

$$
\cos^2(x)= \frac 1 2 ( 1+ \cos(2x))
$$

anonymous · Answer

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

nali · Answer

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

anonymous · Answer

$$
(\cos (2 x)+1)^2=\cos ^2(2 x)+2 \cos (2
   x)+1
$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Did you get it?

nali · Answer

but iam looking for cos^4 2x

nali · Answer

not cos^4 x

anonymous · Answer

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

nali · Answer

thanku so much

anonymous · Answer

yw

nali · Answer

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

anonymous · Answer

No it will not be deleted.

nali · Answer

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

anonymous · Answer

I think so.

nali · Answer

ok thanks again