Question

PLEASE HELP ME!!! I JUST NEED TO KNOW HOW TO DO THIS!!

Verify the identity.

cos(4u)=cos^2(2u) - sin^2(2u)

Answer 1

I made this trig sheet. http://learnix.net/wordpress/wp-content/uploads/Trig-Cheat-Sheet-1.4.pdf Can you see an identity on it that might fit this situation?

Answer 2

I'm really not sure how this is done. This is why I am asking how it can be done

Answer 3

check out on my sheet where it says Angle Sum and Difference Do you see the cosine one, which is second from top?

Answer 4

yes? Could you please tell me how to do it?

Answer 5

like what steps would I take?

Answer 6

So what do we need to do to make cos(4u) to look like cos(x+y) where x and y are anything. Sorry for the delayed response too.

Answer 7

i don't know, please just explain to me

Answer 8

okay, so we can rewrite cos(4u) as cos(2u+2u) right?

Answer 9

yes

Answer 10

According to my cheat sheet you follow the right hand side of the equation now. Can you do that?

Answer 11

no, please just show me how to do it. I'm a visual learning

Answer 12

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Answer 13

\(cos (4u) = cos (2u+2u)\) ok?

Answer 14

okay, why?

Answer 15

not yet, be patient

Answer 16

you got it

Answer 17

cos (a+b) = cos acosb - sina sinb
now, apply to your problem with a = 2u and b = 2u also
you have :
\(cos (4u) = cos (2u+2u) = cos (2u)cos (2u) - sin(2u) sin(2u) = cos^2 (2u) -sin^2 (2u)\)
dat sit.

Answer 18

Thank you!!