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

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

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

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

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

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

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 : x = 2 πn, x = π + 2 πn

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

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

sin (2 θ) = - 3 cos (2 θ)

4 sec (θ) - 4 = 0

sin (2 x) + 6 cos (x) = 0

cos (3 x) = \frac{1}{2}, 0 \leq x \leq 2 π

2 cos^{2} (x) - cos (x) = 0, 0 \leq x < 2 π

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