1) CosX = SinSinX/CosX = TanX = X = π/4 + kπ, где k - целое число
2) 2SinX + CosX = SinX = -CosX/SinX = -√(1-Cos^2 X)/1 - Cos^2 X = 4Sin^2 1 - Cos^2 X = 4 - 4Cos^2 3Cos^2 X = CosX = ±√3/2
X = π/6 + 2kπ, 5π/6 + 2kπ, k - целое число
3) 3Sin^2 X - 7SinXCosX + 2Cos^2 X = (3SinX - 2CosX)(SinX - 1) = 1) 3SinX - 2CosX = SinX = 2CosX/SinX = √(1 - Cos^2 X4 - 4Cos^2 X = 9(1 - Cos^2 X4 - 4Cos^2 X = 9 - 9Cos^2 5Cos^2 X = CosX = ±1
X = 0 + πk, π/2 + πk, k - целое число
2) SinX - 1 = SinX = X = π/2 + 2kπ, k - целое число
4) 2Sin^2 X + 3SinXCosX - 2Cos^2 X = (2SinX - CosX)(SinX + 2CosX) = 1) 2SinX - CosX = SinX = CosX/SinX = √(1 - Sin^2 X)/4 - 4Sin^2 X = Sin^2 4 = 5Sin^2 SinX = ±2/√5
X = arcsin(±2/√5) + 2kπ, k - целое число
2) SinX + 2CosX = SinX = -2CosSinX = √(1 - Cos^2 X1 + 4Cos^2 X = 1 - Cos^2 5Cos^2 X = CosX = 0
X = π/2 + πk, k - целое число
1) CosX = Sin
SinX/CosX = TanX =
X = π/4 + kπ, где k - целое число
2) 2SinX + CosX =
SinX = -CosX/
SinX = -√(1-Cos^2 X)/
1 - Cos^2 X = 4Sin^2
1 - Cos^2 X = 4 - 4Cos^2
3Cos^2 X =
CosX = ±√3/2
X = π/6 + 2kπ, 5π/6 + 2kπ, k - целое число
3) 3Sin^2 X - 7SinXCosX + 2Cos^2 X =
(3SinX - 2CosX)(SinX - 1) =
1) 3SinX - 2CosX =
SinX = 2CosX/
SinX = √(1 - Cos^2 X
4 - 4Cos^2 X = 9(1 - Cos^2 X
4 - 4Cos^2 X = 9 - 9Cos^2
5Cos^2 X =
CosX = ±1
X = 0 + πk, π/2 + πk, k - целое число
2) SinX - 1 =
SinX =
X = π/2 + 2kπ, k - целое число
4) 2Sin^2 X + 3SinXCosX - 2Cos^2 X =
(2SinX - CosX)(SinX + 2CosX) =
1) 2SinX - CosX =
SinX = CosX/
SinX = √(1 - Sin^2 X)/
4 - 4Sin^2 X = Sin^2
4 = 5Sin^2
SinX = ±2/√5
X = arcsin(±2/√5) + 2kπ, k - целое число
2) SinX + 2CosX =
SinX = -2Cos
SinX = √(1 - Cos^2 X
1 + 4Cos^2 X = 1 - Cos^2
5Cos^2 X =
CosX = 0
X = π/2 + πk, k - целое число