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

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

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

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

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = \frac{πn}{2}, x = \frac{π}{4} + \frac{πn}{2}

Solution steps

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

Rewrite using trig identities

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

Solving each part separately

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

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

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

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = \frac{πn}{2}, x = \frac{π}{4} + \frac{πn}{2}

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

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

sin^{2} (θ) = 2 cos (θ) + 2

cos (4 x) (cos (x) - 1) = 0

3 tan (\frac{x}{2}) + 3 = 0

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