What is the general solution for 12sin^2(x)+18sin(x)+6=0 ?

The general solution for 12sin^2(x)+18sin(x)+6=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x=(3pi)/2+2pin

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12sin^2(x)+18sin(x)+6=0

12 sin^{2} (x) + 18 sin (x) + 6 = 0

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

12 sin^{2} (x) + 18 sin (x) + 6 = 0

Solve by substitution

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

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

csc^{2} (θ) + cot (θ) = 0

sin^{2} (θ) - 2 sin (θ) - 3 = 0

5 tan (θ) - 4 = 0

0 = cos (\frac{x}{2})

3 cos (x) - 1 = cos (2 x)

What is the general solution for 12sin^2(x)+18sin(x)+6=0 ?
The general solution for 12sin^2(x)+18sin(x)+6=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x=(3pi)/2+2pin