Find $p,q$ to the expression $A = p (cos^{8}x-sin^{8}x) + 4(cos^{6}x-2sin^{6}x) + qsin^{4}x$ does not depend upon $x$

Question

dan815 · Answer

okay if u dont want it to depend on x, we have to compress this into sin^2 x + cos^2 (x) identity or something similar

dan815 · Answer

... is this what all korean problems in school are like

dan815 · Answer

http://www.sosmath.com/trig/Trig5/trig5/trig5.html here u go have fun

ganeshie8 · Answer

may be try messing wid exponents + binomial thm instead :
$\cos x  = \dfrac{e^{-ix} + e^{ix}}{2}$


$\sin x  = \dfrac{e^{-ix} - e^{ix}}{2}$

dan815 · Answer

complex numbers are really amazing

dan815 · Answer

i shud play with them more often

ganeshie8 · Answer

dan lookup star polygons using complex numbers... i checked that few days back because of @Kainui  and it was really wonderful !

dan815 · Answer

do u mean the fractcal pattern generation with complex numbers?

ganeshie8 · Answer

Yes more specifically about iterations

ganeshie8 · Answer

when u hae time : http://www.mtoliveboe.org/cmsAdmin/uploads/not-so-complex-iteration-in-the-complex-plane.pdf

dan815 · Answer

ok cool

kainui · Answer

Interesting that you mention this @ganeshie8  because I was just thinking about that and looking at star polygons today and thinking about applying them to making knots. Just a little playing around and I discovered that I could make some pretty cool looking knots and use a little bit of complex numbers to play around with them.