Question

Use the half angle formulas to simplify the expression.

-sqrt ((1+cos 8x)/(1-cos 8x))

Answer 1

well can't you use

\[\cos^2(4x) = \frac{1 + \cos(8x)}{2}~~~or~~~2\cos^2(4x) = 1 + \cos(8x)\]

and

\[\sin^2(4x) = \frac{1 - \cos(8x)}{2}~~~~or~~~~2\sin^2(4x) = 1 - \cos(8x)\]

sustitute them and you have

\[- \sqrt{\frac{2\cos^2(4x)}{2\sin^2(4x)}}\]

Answer 2

and then you should be able to work from there

Answer 3

how do you know theyre equal to that?

Answer 4

Not really Im so confused.

Answer 5

Yes, its the half angle one im confused with

Answer 6

Why would I be using the double angle formulas?

Answer 7

I have them I just dont know what to use

Answer 8

So I need to use double angle formulas and not the half angle ones?

Answer 9

ok where do i plug in the expression into the formula

Answer 10

i"ll eliminate all posts so that the information is in sequence... and see if it makes sense.

and

\[-\sqrt{\frac{2\cos^2(4x)}{2\sin^2(4x)}} = -\sqrt{\cot^2(4x)}\]

just simplify from here