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

The general solution for csc^2(θ)-2csc(θ)=0 is θ= pi/6+2pin,θ=(5pi)/6+2pin

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csc^2(θ)-2csc(θ)=0

csc^{2} (θ) - 2 csc (θ) = 0

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

Solution steps

csc^{2} (θ) - 2 csc (θ) = 0

Solve by substitution

csc (θ) = 2, csc (θ) = 0

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

csc (θ) = 0 :

No Solution

Combine all the solutions

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

cos (θ) = - \frac{7}{25}

3 cos (x) + 3 sin (x) tan (x) = 6

tan^{2} (2 x) - 1 = 0

3 sin (4 x) = - 6 sin (2 x)

2 sin (2 θ) - 3 = 0

What is the general solution for csc^2(θ)-2csc(θ)=0 ?
The general solution for csc^2(θ)-2csc(θ)=0 is θ= pi/6+2pin,θ=(5pi)/6+2pin