(sinX)^4 = (3/8) - (1/2)cos(2X) + (1/8)cos(4X)
(cosX)^4 = (3/8) + (1/2)cos(2X) + (1/8)cos(4X)
(sinX)^6 = 5/16 - (15/32)cos(2X) + (6/32)cos(4X) - (1/32)cos(6X)
(cosX)^6 = 5/16 + (15/32)cos(2X) + (6/32)cos(4X) + (1/32)cos(6X)
(sinX)^6 + (cosX)^6 = 5/8 + (3/8)cos(4X)
(sinX)^4 + (cosX)^4 = 6/8 + (2/8)cos(4X)
5/8 + (3/8)cos(4X) = a*(6/8 + (2/8)cos(4X))
5 + 3cos(4X) = a*(6 + 2cos(4X))
(3-2a)cos(4X) = 6a-5 => cos(4X) = (6a-5)/(3-2a)
-1 <= (6a-5)/(3-2a) <=1
1/2 <= a <= 1
Ne znam samo da li ima nekih dodatnih uslova, sad sam poprilično umoram, pa pokušaj sam da proveriš, vidim da ne sme biti a=3/2, ali ta vrednost je izvan dobijenog intervala.
Potpis
Blessed are those who can laugh at themselves, for they shall never cease to be amused.
