cos2x=(1-cosx)/2

Anonym53153501.05.2013 22:12 Nahlásit

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Vlaďka 9894001.05.2013 22:47 (Upr. 01.05.2013 22:48) Nahlásit
2(cos^2(x) - sin^2(x)) = 1 - cos(x)
2cos^2(x) - 2sin^2(x) = 1 - cos(x)
2cos^2(x) - 2sin^2(x) + cos(x) - 1 = 0
2cos^2(x) - 2(1-cos^2(x) + cos(x) - 1 = 0
2cos^2(x) - 2 + 2cos^2(x) + cos(x) - 1 = 0
4cos^2(x) + cos(x) - 3 = 0
s: cos(x) = a
4a^2 + a - 3 = 0
a_(1,2) = (-1 ±√(1+48))/8 = (-1 ± 7)/8
a_1 = 6/8 = 3/4 => cos(x) = 3/4 => x = cca 41°25'+2kπ
a_2 = -1 => cos(x) = -1 => x = 2π + 2kπ
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