1) CosX = SinX
SinX/CosX = TanX = 1
X = π/4 + kπ, где k - целое число

2) 2SinX + CosX = 0
SinX = -CosX/2
SinX = -√(1-Cos^2 X)/2
1 - Cos^2 X = 4Sin^2 X
1 - Cos^2 X = 4 - 4Cos^2 X
3Cos^2 X = 3
CosX = ±√3/2

X = π/6 + 2kπ, 5π/6 + 2kπ, k - целое число

3) 3Sin^2 X - 7SinXCosX + 2Cos^2 X = 0
(3SinX - 2CosX)(SinX - 1) = 0
1) 3SinX - 2CosX = 0
SinX = 2CosX/3
SinX = √(1 - Cos^2 X)
4 - 4Cos^2 X = 9(1 - Cos^2 X)
4 - 4Cos^2 X = 9 - 9Cos^2 X
5Cos^2 X = 5
CosX = ±1

X = 0 + πk, π/2 + πk, k - целое число

2) SinX - 1 = 0
SinX = 1
X = π/2 + 2kπ, k - целое число

4) 2Sin^2 X + 3SinXCosX - 2Cos^2 X = 0
(2SinX - CosX)(SinX + 2CosX) = 0
1) 2SinX - CosX = 0
SinX = CosX/2
SinX = √(1 - Sin^2 X)/2
4 - 4Sin^2 X = Sin^2 X
4 = 5Sin^2 X
SinX = ±2/√5

X = arcsin(±2/√5) + 2kπ, k - целое число

2) SinX + 2CosX = 0
SinX = -2CosX
SinX = √(1 - Cos^2 X)
1 + 4Cos^2 X = 1 - Cos^2 X
5Cos^2 X = 0
CosX = 0

X = π/2 + πk, k - целое число