What is the general solution for 12sin^2(x)-9=0 ?

The general solution for 12sin^2(x)-9=0 is x= pi/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=(5pi)/3+2pin

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12sin^2(x)-9=0

12 sin^{2} (x) - 9 = 0

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

12 sin^{2} (x) - 9 = 0

Solve by substitution

sin (x) = \frac{3}{2}, sin (x) = - \frac{3}{2}

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

sin (x) = - \frac{3}{2} : x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 cos (x - 1) = 0

5 + 6 sin (x) = 0

sin (\frac{π}{2} x) = 0

csc (\frac{θ}{2}) = - \frac{2}{3}

x, - 2 sin (x) + 2 cos (2 x) = 0

What is the general solution for 12sin^2(x)-9=0 ?
The general solution for 12sin^2(x)-9=0 is x= pi/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=(5pi)/3+2pin