What is the general solution for csc^2(θ)-2=0 ?

The general solution for csc^2(θ)-2=0 is θ= pi/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin,θ=(7pi)/4+2pin

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csc^2(θ)-2=0

csc^{2} (θ) - 2 = 0

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

csc^{2} (θ) - 2 = 0

Solve by substitution

csc (θ) = 2, csc (θ) = - 2

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

csc (θ) = - 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

2 sin^{2} (x) + 11 cos (x) = 7

sin (A) = \frac{5}{13}

2 cos (x) = - 2

3 tan (3 x) = 3

cos (\frac{2}{3} x - \frac{π}{2}) - 1 = 0

What is the general solution for csc^2(θ)-2=0 ?
The general solution for csc^2(θ)-2=0 is θ= pi/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin,θ=(7pi)/4+2pin