# Help with Multiple Angle Identities POSSIBLY HELP?

Discussion in 'Random Topic Center' started by OLD_SCHOOL_PLAYER, May 8, 2008. 1. ### OLD_SCHOOL_PLAYERNew Member

Hi everyone, I am looking for some help on math. I looked the solution up in the back of the text book, but I am puzzled on how they are getting that answer. They showed their work but I am just curious on if I am interpreting it right and stuff.

Here is the first problem:

sin^4(x) = 1/8(3 - 4cos2x + cos4x)

= (sin²x)² *I understand this

= [1/2(1-cos2x)]² *I believe they substituted 1-cos²x for sin²x...and then to get rid of the ² on the cos, they took the square root of the equation, so they put times 1/2 instead. LMK if that is the correct way of thinking.

= 1/4(1 - 2cos²x + cos²2x) *I think they foiled out (1-cos2x) (shown down below)

FOILED:
(1-cos2x) (1-cos2x)
= 1 - cos2x - cos2x + cos²2x
= 1 - 2cos2x + cos²2x

= 1/4[1 - 2cos2x + 1/2(1 + cos4x)] *I don't know what happened here where the bold face is at.

= 1/8(2 - 4cos2x + 1 + cos4x) *IDK

= 1/8(3 - 4cos2x + cos 4x) *which is what we were trying to prove

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Second Problem: FINISHED TY TO ARMondak!
Use half-angle identities to find all solutions in the interval [0, 2π)

cos²x = sin²(x/2)

π/3, π, 5π/3

*π = pi symbol just to lyk*

I do not understand how to do this one, if someone can explain it would be mostly appreciated.

Thank you for reading.

Last edited: May 8, 2008
2. Take the right side and substitute ((1-cosx)/2)^1/2 for sin^2 x/2, keeping the square. The square and square root cancel out, leaving you with:

cos^2 x = (1 - cos x)/2

Then multiply both sides by 2

2 cos^2 x = 1 - cos x

Bring everything to the left

2 cos^2 x + cos x - 1 = 0

Factor

(2 cos x - 1) (cos x + 1)

Leaving

cos x = 1/2, -1

Which will give you

x = 60 (n/3) and 240 (5n/3) when cos x = 1/2 and 180 (n) when cos x = -1

Hope this helps.

3. ### OLD_SCHOOL_PLAYERNew Member

I am so sorry but the first line lost me : /

I understand what you do from there but I am a little confused on the first step and how you did it.