What is the general solution for 3+3sin(θ)= 6/(3-2sin(θ)) ?

The general solution for 3+3sin(θ)= 6/(3-2sin(θ)) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin,θ= pi/2+2pin

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3+3sin(θ)= 6/(3-2sin(θ))

3 + 3 sin (θ) = \frac{6}{3 - 2 sin ( θ )}

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

Solution steps

3 + 3 sin (θ) = \frac{6}{3 - 2 sin ( θ )}

Solve by substitution

sin (θ) = - \frac{1}{2}, sin (θ) = 1

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

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

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

cos (x) = - 0.07

2 tan (θ) + 9 = 0

cos (x) = - 0.73

5 cos^{2} (x) - 3 cos (x) = 2

9 tan^{2} (x) - 27 = 0

What is the general solution for 3+3sin(θ)= 6/(3-2sin(θ)) ?
The general solution for 3+3sin(θ)= 6/(3-2sin(θ)) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin,θ= pi/2+2pin