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

The general solution for csc^2(θ)=cot(θ)+1 is θ= pi/4+pin,θ= pi/2+pin

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csc^2(θ)=cot(θ)+1

csc^{2} (θ) = cot (θ) + 1

θ = \frac{π}{4} + πn, θ = \frac{π}{2} + πn

Solution steps

csc^{2} (θ) = cot (θ) + 1

Subtract

cot (θ) + 1

from both sides

csc^{2} (θ) - cot (θ) - 1 = 0

Rewrite using trig identities

- cot (θ) + cot^{2} (θ) = 0

Solve by substitution

cot (θ) = 1, cot (θ) = 0

cot (θ) = 1 : θ = \frac{π}{4} + πn

cot (θ) = 0 : θ = \frac{π}{2} + πn

Combine all the solutions

θ = \frac{π}{4} + πn, θ = \frac{π}{2} + πn

7 cos (x) tan (x) = - 8 tan (x)

4 sin (θ) - 1 = 2 sin (θ) + 1

3 sec^{2} (2 x) = 4

4 cot (x) = cot (x) sin^{2} (x)

arctan (x) = - 1

What is the general solution for csc^2(θ)=cot(θ)+1 ?
The general solution for csc^2(θ)=cot(θ)+1 is θ= pi/4+pin,θ= pi/2+pin