Question

6sin^(x)+5cos(x)-2=0

Answer 1

6sin^(x)+5cos(x)-2=0
6(1- cos^(x))+5cos(x)-2=0
6-6cos^(x)+5cos(x)-2=0
-6cos^(x)+5cos(x)+4=0 /:(-1)
6cos^(x) - 5cos(x) - 4=0
D=25+4*6*4=121 = 11^2
cosx = (5+11)/12 = 16/12 = 4/3 ===> нет реш.
cosx = (5-11)/12 = -6/12 = -1/2 ===> x = ± 2pi/3 + 2pik,k c Z

ОТВЕТ: ± 2pi/3 + 2pik,k c Z