sin^2(X) - 3sinxcosXx + 2cos^2(x) = 0
x = П/4 + Пn, где n принадлежит всем целым числам.
а) 2sin2x-1 = 0, sin2x = 1/2
2x = (-1)^n*arcsin1/2 + πn
2x = (-1)^n *π/6 + πn
x = (-1)^n* π/12 + πn/2
б) cos²x - cosx = 0
cosx(cosx-1) = 0
б.1) cosx = 0
x = π/2 + πn
б.2) cosx -1 = 0
cosx = 1
x = 2πn
15(sin^2x + 2sinx + 1) = 17 + 31sinx
15sin^2x + 30sinx + 15 = 17 + 31sinx
15sin^2x + 30sinx + 15 - 17 - 31sinx = 0
15sin^2x - sinx - 2 = 0
sinx=t, t ∈ [ - 1; 1]
15t^2 - t - 2 = 0
D = 1 + 4*30 = 121
t1 = ( 1 + 11)/30 = 12/30 = 2/5
t2 = ( 1 - 11)/30 = - 10/30 = - 1/3
sinx = 2/5
x = (-1)^k arcsin (2/5) + pik. k ∈Z
sinx = - 1/3
x = (-1)^(k+1) arcsin(1/3) + pik. k ∈Z
sinx=√3/2
x1=π/3+2πk
x2=2π/3+2πk , kэZ
sin^2(X) - 3sinxcosXx + 2cos^2(x) = 0
x = П/4 + Пn, где n принадлежит всем целым числам.
а) 2sin2x-1 = 0, sin2x = 1/2
2x = (-1)^n*arcsin1/2 + πn
2x = (-1)^n *π/6 + πn
x = (-1)^n* π/12 + πn/2
б) cos²x - cosx = 0
cosx(cosx-1) = 0
б.1) cosx = 0
x = π/2 + πn
б.2) cosx -1 = 0
cosx = 1
x = 2πn