Sin2x + V2 sinx = 0
2sin x cos x + V2 sinx = 0
sinx (2 cos x + V2) = 0
a)sinx = 0 , 2cos x= -V2
x = pin, n E z
2cos x = -V2
cos x = -V2/2
x = +-3pi/4 + 2pin, n E z
n = 1
x1 = pi
x2 = +-3pi/4 + 2pi = 2pi - 3pi/4 = 5pi/4
n=0
x3 = +-3pi/4
Ответ pi, 5pi/4, +-3pi/4
б) V3cos^2 x - 0,5 cos(3pi/2 + 2x) = V3cos^2 x - 0.5 sin2x = V3cos^2x - sin x cos x = cos x (V3 cos x - sinx)
в) cos2x = Tg^2 x - cos^2 x
cos^2 x - sin^2 x = tg^2 x - cos^2 x
2cos^2 x - sin^2 x = tg^2 x
cos x <= 1/2<br>x <= +- pi/6 + 2pin