What is the general solution for 12sin^2(θ)=9 ?

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

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12sin^2(θ)=9

12 sin^{2} (θ) = 9

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

Solution steps

12 sin^{2} (θ) = 9

Solve by substitution

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

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

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

Combine all the solutions

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

2 cos (x) + 3 = 0, 0 \leq x \leq 2 π

\frac{cot ^{2} ( x )}{1 + sin ( x )} = \frac{csc ( x ) - 1}{sin ^{2} ( x )}

tan (x) = 2.3

2 sec^{2} (x) = 5 tan (x) + 5

tan^{2} (x) - 2 tan (x) = 3

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