What is the general solution for 6sin^2(x)-9sin(x)+3=0 ?

The general solution for 6sin^2(x)-9sin(x)+3=0 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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6sin^2(x)-9sin(x)+3=0

6 sin^{2} (x) - 9 sin (x) + 3 = 0

x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

6 sin^{2} (x) - 9 sin (x) + 3 = 0

Solve by substitution

sin (x) = 1, sin (x) = \frac{1}{2}

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

cos (2 x) = 0.25

3 cos^{2} (x) = 2

3 tan (θ) = 2 sin (θ)

sin (x) = - 0.1

189.4 = 100 tan^{2} (4 5^{\circ} + \frac{θ}{2})

What is the general solution for 6sin^2(x)-9sin(x)+3=0 ?
The general solution for 6sin^2(x)-9sin(x)+3=0 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin