What is the general solution for 3csc^2(θ)=1+2csc^2(θ) ?

The general solution for 3csc^2(θ)=1+2csc^2(θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin

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3csc^2(θ)=1+2csc^2(θ)

3 csc^{2} (θ) = 1 + 2 csc^{2} (θ)

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

Solution steps

3 csc^{2} (θ) = 1 + 2 csc^{2} (θ)

Solve by substitution

csc (θ) = 1, csc (θ) = - 1

csc (θ) = 1 : θ = \frac{π}{2} + 2 πn

csc (θ) = - 1 : θ = \frac{3 π}{2} + 2 πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

tan^{2} (x) = 2

0 = 2 cos (2 x)

4 cos^{4} (x) - 5 cos^{2} (x) + 1 = 0

3 sin (x) + 2 = sin (x)

sin (x) cos (x) - sin (x) = 0

What is the general solution for 3csc^2(θ)=1+2csc^2(θ) ?
The general solution for 3csc^2(θ)=1+2csc^2(θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin