What is the general solution for cot^2(θ)-3csc(θ)+3=0 ?

The general solution for cot^2(θ)-3csc(θ)+3=0 is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ= pi/2+2pin

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cot^2(θ)-3csc(θ)+3=0

cot^{2} (θ) - 3 csc (θ) + 3 = 0

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 = 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

x, arctan (x) + arctan (y) = \frac{π}{2}

2 sin (x) = 2 sin (2 x)

3 cos (2 x) - 1 = 0

2 cos^{2} (x) = 2

0 = - 2 sin (t) - 4 cos (2 t)

What is the general solution for cot^2(θ)-3csc(θ)+3=0 ?
The general solution for cot^2(θ)-3csc(θ)+3=0 is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ= pi/2+2pin