What is the general solution for sin(6x)-sin(2x)=0 ?

The general solution for sin(6x)-sin(2x)=0 is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2 ,x=pin,x= pi/2+pin

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sin(6x)-sin(2x)=0

sin (6 x) - sin (2 x) = 0

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}, x = πn, x = \frac{π}{2} + πn

Solution steps

sin (6 x) - sin (2 x) = 0

Rewrite using trig identities

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

Solving each part separately

cos (4 x) = 0 or sin (2 x) = 0

cos (4 x) = 0 : x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}

sin (2 x) = 0 : x = πn, x = \frac{π}{2} + πn

Combine all the solutions

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}, x = πn, x = \frac{π}{2} + πn

z, cos (x) + cos (y) + cos (z) = 0

12 sin^{2} (x) + cos (x) - 6 = 0

2 sin (2 θ) - 1 = 0

cos (\frac{1}{x}) = 0

y, x = sinh (y)

What is the general solution for sin(6x)-sin(2x)=0 ?
The general solution for sin(6x)-sin(2x)=0 is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2 ,x=pin,x= pi/2+pin