ubisoft
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Prove

cos(x+\frac{1}{4}n\pi ) - sin(x+\frac{1}{4}\ n\pi ) = \sqrt{2}  cos(x+\frac{1}{4}(n+1)\pi ))}
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TenOfThem
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#2
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(Original post by ubisoft)
Prove

cos(x+\frac{1}{4}n\pi ) - sin(x+\frac{1}{4}\ n\pi ) = \sqrt{2}  cos(x+\frac{1}{4}(n+1)\pi ))}
Just use harmonic form

Cos(y) - Sin(y) = R Cos(y+a)


R will be \sqrt2

a will be \dfrac{\pi}{4}
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ubisoft
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(Original post by TenOfThem)
Just use harmonic form
Haven't done that yet as I'm still on C3...

EDIT: how do you work out R and a?
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TenOfThem
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(Original post by ubisoft)
Haven't done that yet as I'm still on C3...

EDIT: how do you work out R and a?
Ok

Start with the RHS

\sqrt2 \cos((x+\frac{n}{4}\pi) + \frac{\pi}{4})


So Cos(A+B) where B = \frac{\pi}{4}
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white slave
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#5
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math is sexy!
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ubisoft
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#6
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(Original post by TenOfThem)
Ok

Start with the RHS

\sqrt2 \cos((x+\frac{n}{4}\pi) + \frac{\pi}{4})


So Cos(A+B) where B = \frac{\pi}{4}
So then do you use the double angle properties to split it up?
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TenOfThem
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#7
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(Original post by ubisoft)
So then do you use the double angle properties to split it up?
The compound angle rules, yes
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ubisoft
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#8
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(Original post by TenOfThem)
The compound angle rules, yes
Thanks, I've done it now. It was from a proof by induction question from FP2, I had to look up the harmonic form thing and it became clear.
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