What is the general solution for sin^2(3x)-sin^2(x)=0 ?

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

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sin^2(3x)-sin^2(x)=0

sin^{2} (3 x) - sin^{2} (x) = 0

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

Solution steps

sin^{2} (3 x) - sin^{2} (x) = 0

Factor

sin^{2} (3 x) - sin^{2} (x) : (sin (3 x) + sin (x)) (sin (3 x) - sin (x))

(sin (3 x) + sin (x)) (sin (3 x) - sin (x)) = 0

Solving each part separately

sin (3 x) + sin (x) = 0 or sin (3 x) - sin (x) = 0

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

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

Combine all the solutions

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

Merge Overlapping Intervals

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

sec^{2} (x) + 6 tan (x) + 4 = 0

1 - 2 tan^{2} (θ) = - tan^{2} (θ)

cos (a) = \frac{1}{3}

2 cos (2 θ) = 3

2 sin^{2} (θ) - 5 sin (θ) + 2 = 0

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