What is the general solution for 6sin^2(θ)=3 ?

The general solution for 6sin^2(θ)=3 is θ= pi/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin,θ=(7pi)/4+2pin

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6sin^2(θ)=3

6 sin^{2} (θ) = 3

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

Solution steps

6 sin^{2} (θ) = 3

Solve by substitution

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

sin (θ) = \frac{1}{2} : θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

sin (θ) = - \frac{1}{2} : θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

Combine all the solutions

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

6 sin^{2} (θ) = 2

10 tan (θ) + 9 = 0

189.4 = 100 tan^{2} (4 5^{\circ} - \frac{x}{2})

5 = sin (x)

\frac{20}{3} sin (10 x) + 5 cos (10 x) = 0

What is the general solution for 6sin^2(θ)=3 ?
The general solution for 6sin^2(θ)=3 is θ= pi/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin,θ=(7pi)/4+2pin