Proving the Cosine Identity: 5/16 + 15/32(cos2x) + 3/16(cos4x) + 1/32(cos6x)

[banfill_89]

yet another trig identity...

Homework Statement

prove: cos^(x)= 5/16+15/32(cos2x)+3/16(cos4x)+1/32(cos6x)

Homework Equations

The Attempt at a Solution

i attempted to use the formula cos^2(x)=(1+cos2x)/(2), and square both sides, then use it again for the square roots, then multiply the answer by (1+cos2x)/(2) again thus making the left side cos^6.....not getting the right answer

 

[banfill_89]

i think I am on the right trrack?

 

[Defennder]

You mean cos^2 (x) on the left?

 

[banfill_89]

hey...the original proof is cos^6(x) on the left side

 

[banfill_89]

i get to a certain point where i get like...cos^2(4x) times cos (2x) wth a bunch of other stuff on the left...but i don't knwo what to do with it

 

[Defennder]

Oh yeah, should have read it more closely. I haven't tried it out yet, but if you know the left is function of cos x only, you should repeatedly apply the double angle cos and sin formula to change everything to functions of sin x and cos x. Then express those functions of sin x as functions of cos x. It should all cancel out.

 

[banfill_89]

lol its cool...so wadda u think? do you get what i tried to do? like is it clear when i explained it?

 

[banfill_89]

thats what i keep doing...

 

[Defennder]

I just proved it using the approach suggested earlier. Just convert everything on the right to a function of cos x. A lot of terms will cancel out to give cos^6 x.