Question

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

cos^4 2x

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

Did you get it?

Answer 9

but iam looking for cos^4 2x

Answer 10

not cos^4 x

Answer 11

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

Answer 12

thanku so much

Answer 13

yw

Answer 14

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

Answer 15

No it will not be deleted.

Answer 16

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

Answer 17

I think so.

Answer 18

ok thanks again