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

The general solution for csc^2(θ)=4 is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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csc^2(θ)=4

csc^{2} (θ) = 4

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solution steps

csc^{2} (θ) = 4

Solve by substitution

csc (θ) = 2, csc (θ) = - 2

csc (θ) = 2 : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

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

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

sin (θ) cos (θ) = \frac{1}{4}

cos^{2} (x) + 13 cos (x) = 14

3 tan (θ) = 33

sin (x) = - \frac{5}{3}

tan (a) = 2.4

What is the general solution for csc^2(θ)=4 ?
The general solution for csc^2(θ)=4 is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ=(7pi)/6+2pin,θ=(11pi)/6+2pin