Question

5 cos^4 (6x)

Which identity do I use, and how do I work the problem?

Answer 1

you need to simplify it?

Answer 2

Yes

Answer 3

I was going to use cos2x = (1+cos(2x))/2

Answer 4

but I am just having trouble with the operations

Answer 5

i think you have written wrong
you can use the identity\[\cos2x=2\cos ^{2}x-1\]

Answer 6

So it would look like 5(2cos^2(6x)-1)^2

Is that right?

Answer 7

from this you will get\[\frac{ 5 }{ 2 }*[ 1+\cos12x] \]

Answer 8

do you get that

Answer 9

in the above identity of cos2x,
replace \[\cos ^{2}x\]
with\[\cos ^{2}6x\]
you get
1+cos2(6x)

Answer 10

one mistake

Answer 11

Not cos(12x) - 1? From using the identity cos2x = 2cos^2 (x) - 1

Answer 12

see ther is \[\cos ^{2}x\]
which is to be replaced by\[\cos ^{2}6x\]
in the identity

Answer 13

sorry and the correct ans. is

Answer 14

\[5*(\frac{ 1+\cos12x }{ 2 })^{2}\]

Answer 15

what is the thing which you dont got

Answer 16

why there is a 2 in the denominator?

Answer 17

I think we are talking about different identities now

Answer 18

If we use cos^2 (x) = (1+cos2x)/2

Then we have 5((1+cos(12x))/2)^2

Answer 19

I understand it like that

Answer 20

I was going to use cos2x = (1+cos(2x))/2-------------this is that which you had written

here cos2x in LHS is \[\cos ^{2}x\]

Answer 21

Oh ok, I understand then. I thought you were using cos2x = 2cos^2 x - 1 That is what you wrote at the beginning. But I understand now. Thank you!

Answer 22

yes what you have written is correct

Answer 23

and then i FOIL those terms, distribute the 5 back in and badabing, I have my answer right?

Answer 24

did the ans. match with that in ans. book

Answer 25

The answer in the book is

Answer 26

@dan815

Answer 27

@iambatman

Answer 28

I have the answer, with the work

Answer 29

@lall thank you!

Answer 30

nice!