Question

I'm so bad at these please help:

Verify the identity.

cos 4x + cos 2x = 2 - 2 sin2 2x - 2 sin2 x

Answer 1

wait ...is it

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

?

Answer 2

I'm going to assume what I wrote is indeed what you intended to put...because it checks out.

So you should know your double angle identities, and use them on both cos(4x) and cos(2x)

I'll wait until you're back to continue

Answer 3

ah im sorry! i was working on another problem. its cos 4x + cos 2x = 2 - 2 sin^2 2x - 2 sin^2 x

Answer 4

Right...so yeah same thing * sin^2 (2x)) is the same as sin(2x)^2 * :)

so okay....on with the problem

Answer 5

oh ok

Answer 6

So you can use the double angle identities on both cos(4x) and cos(2x) ....what would that look like?

Answer 7

or at least....what is the double angle identity applied to cos(2x)?

Answer 8

im not really sure.. is it cosa-sina?

Answer 9

here's a little push in the right direction :)

cos(2x) = 1 - 2sin(x)^2
cos(4x) = 1 - 2sin(2x)^2

okay?

Answer 10

ok sorry im looking at it, i havent really done one like this before

Answer 11

no problem :) just hope it'll be understandable :)

so now you have

1-2sin(x)^2 + 1-2sin(2x)^2 = 2 - 2sin(2x)^2 - 2sin(x)^2

What happens when we combine the left hand side?

1-2sin(x)^2 + 1-2sin(2x)^2 ?

Answer 12

*hint...the only thing you can combine is 1 + 1 :)

Answer 13

ok so that's how you get 2-2sinx^2-2sin2x^2..
got it! thank you, sorry i dont know why i was so confused before haha :)

Answer 14

No problem :) trig identities can be a hassle so don't worry about getting confused every once in a while :)