What is the general solution for csc(θ)-cot^2(θ)+1=0 ?

The general solution for csc(θ)-cot^2(θ)+1=0 is θ=(3pi)/2+2pin,θ= pi/6+2pin,θ=(5pi)/6+2pin

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csc(θ)-cot^2(θ)+1=0

csc (θ) - cot^{2} (θ) + 1 = 0

θ = \frac{3 π}{2} + 2 πn, θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solution steps

csc (θ) - cot^{2} (θ) + 1 = 0

Rewrite using trig identities

2 + csc (θ) - csc^{2} (θ) = 0

Solve by substitution

csc (θ) = - 1, csc (θ) = 2

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

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

Combine all the solutions

θ = \frac{3 π}{2} + 2 πn, θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin (x - 4 0^{\circ}) = 1

sin (x) = - cos (x), - 2 π \leq x \leq 2 π

sin (θ) = - \frac{7}{8}

sin^{2} (x) sec (x) cot (x) = \frac{3}{2}

x, sin (y) = y cos (2 x)

What is the general solution for csc(θ)-cot^2(θ)+1=0 ?
The general solution for csc(θ)-cot^2(θ)+1=0 is θ=(3pi)/2+2pin,θ= pi/6+2pin,θ=(5pi)/6+2pin