What is the general solution for cot^2(θ)-3csc(θ)=-3 ?

The general solution for cot^2(θ)-3csc(θ)=-3 is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ= pi/2+2pin

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cot^2(θ)-3csc(θ)=-3

cot^{2} (θ) - 3 csc (θ) = - 3

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

Solution steps

cot^{2} (θ) - 3 csc (θ) = - 3

Subtract

- 3

from both sides

cot^{2} (θ) - 3 csc (θ) + 3 = 0

Rewrite using trig identities

2 + csc^{2} (θ) - 3 csc (θ) = 0

Solve by substitution

csc (θ) = 2, csc (θ) = 1

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

csc (θ) = 1 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

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

tan^{3} (x) = \frac{1}{3} tan (x)

cos^{2} (x) = \frac{2}{3}

5 ∣ tan (x) ∣ = 5

3 arccos (x) = 2

cos (4 x) = - \frac{1}{2}, 0 \leq x \leq 2 π

What is the general solution for cot^2(θ)-3csc(θ)=-3 ?
The general solution for cot^2(θ)-3csc(θ)=-3 is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ= pi/2+2pin