What is the general solution for sin^2(3x)=1 ?

The general solution for sin^2(3x)=1 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3

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sin^2(3x)=1

sin^{2} (3 x) = 1

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

Solution steps

sin^{2} (3 x) = 1

Solve by substitution

sin (3 x) = 1, sin (3 x) = - 1

sin (3 x) = 1 : x = \frac{π}{6} + \frac{2 πn}{3}

sin (3 x) = - 1 : x = \frac{π}{2} + \frac{2 πn}{3}

Combine all the solutions

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

2 - - 1 - 6 sin (x) = - 4 sin (x)

2 sin (\frac{x}{2}) - 1 = 0

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

2 tan^{2} (t) = - 3 sec (t)

tan^{2} (x) + 3 = 0

What is the general solution for sin^2(3x)=1 ?
The general solution for sin^2(3x)=1 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3