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

The general solution for sin(2x)-sqrt(2)sin(x)=0,0<= x<= 2pi is x=0,x=pi,x=2pi,x= pi/4 ,x=(7pi)/4

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sin(2x)-sqrt(2)sin(x)=0,0<= x<= 2pi

sin (2 x) - 2 sin (x) = 0, 0 \leq x \leq 2 π

x = 0, x = π, x = 2 π, x = \frac{π}{4}, x = \frac{7 π}{4}

Solution steps

sin (2 x) - 2 sin (x) = 0, 0 \leq x \leq 2 π

Rewrite using trig identities

- sin (x) 2 + 2 cos (x) sin (x) = 0

Factor

- sin (x) 2 + 2 cos (x) sin (x) : sin (x) (- 2 + 2 cos (x))

sin (x) (- 2 + 2 cos (x)) = 0

Solving each part separately

sin (x) = 0 or - 2 + 2 cos (x) = 0

sin (x) = 0, 0 \leq x \leq 2 π : x = 0, x = π, x = 2 π

- 2 + 2 cos (x) = 0, 0 \leq x \leq 2 π : x = \frac{π}{4}, x = \frac{7 π}{4}

Combine all the solutions

x = 0, x = π, x = 2 π, x = \frac{π}{4}, x = \frac{7 π}{4}

2 sin (x - \frac{π}{3}) + 3 = 0

sin (x) = 0.77

sin (x) = 0.87

sin (x) = 0.14

sin (x) = 0.41

What is the general solution for sin(2x)-sqrt(2)sin(x)=0,0<= x<= 2pi ?
The general solution for sin(2x)-sqrt(2)sin(x)=0,0<= x<= 2pi is x=0,x=pi,x=2pi,x= pi/4 ,x=(7pi)/4