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

The general solution for cot^2(θ)+csc(θ)=1 is θ= pi/2+2pin,θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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cot^2(θ)+csc(θ)=1

cot^{2} (θ) + csc (θ) = 1

θ = \frac{π}{2} + 2 πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solution steps

cot^{2} (θ) + csc (θ) = 1

Subtract

1

from both sides

cot^{2} (θ) + csc (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{π}{2} + 2 πn

csc (θ) = - 2 : θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

5 cos^{2} (θ) - 2 cos (θ) = 0

tan^{2} (x) - 2 tan (x) - 3 = 0

6 cos (x) - 3 = 0

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

2 tan^{2} (x) - tan (x) - 6 = 0

What is the general solution for cot^2(θ)+csc(θ)=1 ?
The general solution for cot^2(θ)+csc(θ)=1 is θ= pi/2+2pin,θ=(7pi)/6+2pin,θ=(11pi)/6+2pin