Question

Verify the identity.

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

Answer 1

\[\cos \left( 4u\right) = \cos ^{2}\left( 2u \right) - \sin ^{2}\left( 2u \right)\]

Answer 2

@Luigi0210

Answer 3

@Hero

Answer 4

@arindameducationusc

Answer 5

@kaitlyn_nicole

Answer 6

@kaitlyn_nicole

Answer 7

@Michele_Laino

Answer 8

Do you know Cos2theta= cos^2theta-sin^2theta?

Answer 9

yes, double angle identity

Answer 10

hint:
we can rewrite the left side as below:
\[\Large \cos \left( {4u} \right) = \cos \left( {2u + 2u} \right)\]

Answer 11

now you can apply the formula of addition for cosine function

Answer 12

\[\Large \cos \left( {x + y} \right) = \cos x\cos y - \sin x\sin y\]

Answer 13

cos ( 2u + 2u ) = cos (2u) cos (2u) - sin (2u) sin (2u) ?

Answer 14

that's right!

Answer 15

what do i do from there?

Answer 16

it is simple, since:
\[\Large \cos \left( {2u} \right)\cos \left( {2u} \right) = {\left( {\cos \left( {2u} \right)} \right)^2}\]

Answer 17

similarly for sin(2u)*sin(2u)

Answer 18

sin(2u) sin(2u) = (sin(2u))^2 ?

Answer 19

yes!

Answer 20

okay, so since im trying to verify this identity, what else do i do to get the answer to look like cos(4u) = cos(4u) ?

Answer 21

since we have proven that left side is equal to right side, then we are done here

Answer 22

so is the final answer cos ( 2u + 2u ) = cos (2u) cos (2u) - sin (2u) sin (2u)
or
cos(2u) cos(2u) = (cos(2u))^2 ?

Answer 23

the answer is the entire procedure which shows how to get the right side, starting from left side

Answer 24

ahhhhhh, i see, i see. thank you soooooo much for your help!

Answer 25

:)