Question

verifying an identity? I need the work please
I'll give medal and fan

see picture below

Answer 1

USE:
\(\color{midniblue}{ \cos(2a)=\cos^2(a)-\sin^2(a)}\)

for,
\(\color{midniblue}{ \cos^2(4x)}\)

Answer 2

where is cos^2(4x)

Answer 3

I mean for, \(\color{midniblue}{ \cos(4x)}\)

Answer 4

not cos(4x) squared, excuse me for that

Answer 5

and thats all?

Answer 6

well, not really, but: that rule can also be written as:
\(\color{midniblue}{ \cos(2a)=1-2\sin^2(a)}\)

Answer 7

\(\color{midniblue}{ \cos(4x)=1-2\sin^2(2x)}\)

Answer 8

and:
\(\color{midniblue}{ \cos(2x)=1-2\sin^2(x)}\)

Answer 9

can u help me simplify the whole thing though?

Answer 10

So,
\(\color{midniblue}{ \cos(4x)+\cos(2x)=(1-
2\sin^2 2x)+(1-2\sin^2~x)}\)

Answer 11

re-write it, and there you go...

Answer 12

rewrite it how

Answer 13

remove parenthesis and add like terms

Answer 14

ok thanks can u check my answer tho? one sec

Answer 15

ok

Answer 16

right now i have: cos(4x)+cos(2x)= 1−2sin^2 2x+ 1−2 sin^2 x

Answer 17

can 1-2sin^2 cancel out

Answer 18

yes that is equal to? (add the 1's)

Answer 19

no sin^2(2x) and sin^2(x) do NOT cancel

Answer 20

ok

Answer 21

they are not like terms, because they are not a sin of a same angle. one is sin of (x0 and the other of (2x).

Answer 22

but you have the 1's to add.....

tell me what you get after doing so

Answer 23

ugh it doesnt let me copy paste

Answer 24

yes, and this way we have verified the idenitiy.

Answer 25

okk thanks so much!

Answer 26

oh, yw