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

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

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

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

sin (2 x) = - 2 cos (x)

cos^{3} (x) + cos^{2} (x) - cos (x) = 1

6 sin (2 x) sin (x) = 6 cos (x)

- 3 cos^{2} (θ) + 11 = - 5 sin (θ) + 6

sin (θ) = - 0.45

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