Question

Please Help Establish!!!
cos2(2u)−sin2(2u)=cos(4u)

Answer 1

cos^2(2u)−sin^2(2u)=cos(4u)

Answer 2

\[\cos^2(2u)-\sin^2(2u)=\cos(4u)\]

Answer 3

Is this the correct relationship you are trying to establish?

Answer 4

Yes

Answer 5

hmm. you know this identity?
\(sin^2x = 1 - cos^2x\)
and
\(cos^2x = \dfrac{1+cos(2x)}{2}\)

Answer 6

Erisu Nakayama, I'd start by working on the right hand side - use the angle reduction formula.

Answer 7

what is angle reduction formula?

Answer 8

The one you gave, power reduction formula, same thing.

Answer 9

so I get
[-1+cos(2u)+cos^2(2u) ]/2

Answer 10

actually -1+cos^2(2u)+cos^2(2u) = 2cos^2(2u) - 1

Answer 11

use\[\Large \cos^2(2x) = \frac{ 1+\cos(4x) }{ 2 }\]
also, she's pretttyyy: http://cdn.wallgig.net/2013/12/31/k0oxed3c_wallpaper_2943511.jpg

Answer 12

now for cos^2(2u), apply second identity i gave you.

Answer 13

oh I got it thanks!

Answer 14

glad we helped

Answer 15

so i get
-.5 + cos(4x)+.5cos^2(4x)

Answer 16

huh?

\(2cos^2(2u) - 1 \\ = 2\left(\dfrac{cos(4u)+1}{2}\right)-1\)

Answer 17

2 cancel each other and 1 and -1 cancel each other so that left you cos(4u)