1) 1 - sin x = Sin x 2Sin x = 1 Sin x = 1/2 x = (-1)^n arcSin 1/2 + nπ, n∈Z x = (-1)^n π/6 + nπ,n∈Z 2) 2 Cos x = 2 Cos x = 1 x = 2πk , k∈Z 3) 5 - 5 Sin x = Cos2x 5 - 5Sin x = 1 - 2Sin² x 2 Sin² x -5Sin x +4 = 0 Sin x = t 2t² - 5t +4 = 0 D = 1 t1= 3/2 t2 = 1 a) Sin x = 3/2 нет решений б) Sin x = 1 x = π/2 + 2πk , k∈Z
2Sin x = 1
Sin x = 1/2
x = (-1)^n arcSin 1/2 + nπ, n∈Z
x = (-1)^n π/6 + nπ,n∈Z
2) 2 Cos x = 2
Cos x = 1
x = 2πk , k∈Z
3) 5 - 5 Sin x = Cos2x
5 - 5Sin x = 1 - 2Sin² x
2 Sin² x -5Sin x +4 = 0
Sin x = t
2t² - 5t +4 = 0
D = 1
t1= 3/2
t2 = 1
a) Sin x = 3/2
нет решений
б) Sin x = 1
x = π/2 + 2πk , k∈Z