What is the general solution for sqrt(2)sin^2(x)-sin(x)=0 ?

The general solution for sqrt(2)sin^2(x)-sin(x)=0 is x= pi/4+2pin,x=(3pi)/4+2pin,x=2pin,x=pi+2pin

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sqrt(2)sin^2(x)-sin(x)=0

2 sin^{2} (x) - sin (x) = 0

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

2 sin^{2} (x) - sin (x) = 0

Solve by substitution

sin (x) = \frac{2}{2}, sin (x) = 0

sin (x) = \frac{2}{2} : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = 2 πn, x = π + 2 πn

cos (2 x) = - 0.35

0 = 3 sin (x + \frac{π}{2})

- cos (t) = cos (t)

sin^{2} (x) - cos (2 x) = - \frac{1}{4}

2 = cos^{2} (x) + sin^{2} (x)

What is the general solution for sqrt(2)sin^2(x)-sin(x)=0 ?
The general solution for sqrt(2)sin^2(x)-sin(x)=0 is x= pi/4+2pin,x=(3pi)/4+2pin,x=2pin,x=pi+2pin