(sin x)^2-sinx*cosx=sinx
(Sin x)^2 - (Cos x+1)Sin x = 0
Sin x=0
Sin x = 0
X = Pik
Or
Sin x - Cos x = 1 / ^2
1-2Sin xCos x = 1
Sin 2x = 0
x = Pik/2

Final Answer: X = Pik/2

3sin2x+2=cos4x
3Sin 2x + 2 = 1-2Sin ^2 2x
2Sin ^2 2x + 3Sin 2x + 1 = 0
2Sin ^2 2x + 2Sin 2x + Sin 2x + 1 = 0
2Sin 2x(Sin 2x+1) + 1(Sin 2x + 1)=0
(2Sin 2x+1)(Sin 2x+1) = 0
Sin 2x = -0.5
Or
Sin 2x = -1

sin(2x+30)+sqrt(3)*sin(60-2x) = 1
We would use the following identity:
Sin a = Cos (Pi/2 - a);
We'll get:
Cos(90-2x-30) + Sqrt(3)Sin(60-2x) = 1
Cos(60-2x) + Tan 60 * Sin(60-2x) = 1
Cos(60-2x)Cos 60 + Sin 60*Sin (60-2x) = 1

Cos = Cos(-2x) = Cos (2x) = 1
Done.