What is the general solution for 4sin^2(θ)=3 ?

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

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4sin^2(θ)=3

4 sin^{2} (θ) = 3

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

4 sin^{2} (θ) = 3

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

cos (2 x) = sin (x) + 1

sec^{2} (x) - sec (x) - 2 = 0

tan^{2} (x) = 0

tan (θ) = - \frac{1}{3}

tan^{2} (x) + tan (x) - 30 = 0

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