What is the general solution for sin(4x)-sin(2x)=0 ?

The general solution for sin(4x)-sin(2x)=0 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3 ,x=2pin,x=pi+2pin

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sin(4x)-sin(2x)=0

sin (4 x) - sin (2 x) = 0

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}, x = 2 πn, x = π + 2 πn

Solution steps

sin (4 x) - sin (2 x) = 0

Rewrite using trig identities

2 cos (3 x) sin (x) = 0

Solving each part separately

cos (3 x) = 0 or sin (x) = 0

cos (3 x) = 0 : x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}, x = 2 πn, x = π + 2 πn

4 sin^{2} (θ) - 3 = 0

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

csc (\frac{7 π}{6})

cos (\frac{4 π}{3})

cos (3 x) = 1

What is the general solution for sin(4x)-sin(2x)=0 ?
The general solution for sin(4x)-sin(2x)=0 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3 ,x=2pin,x=pi+2pin