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

The general solution for (cot(θ)-1)(csc(θ)-1)=0 is θ= pi/4+pin,θ= pi/2+2pin

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(cot(θ)-1)(csc(θ)-1)=0

(cot (θ) - 1) (csc (θ) - 1) = 0

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

Solution steps

(cot (θ) - 1) (csc (θ) - 1) = 0

Solving each part separately

cot (θ) - 1 = 0 or csc (θ) - 1 = 0

cot (θ) - 1 = 0 : θ = \frac{π}{4} + πn

csc (θ) - 1 = 0 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

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

(tan (θ) - 1) (sec (θ) + 1) = 0

9 cos (x) - 9 sin (x) = 0

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

sec^{2} (x) + 6 tan (x) + 4 = 0

1 - 2 tan^{2} (θ) = - tan^{2} (θ)

What is the general solution for (cot(θ)-1)(csc(θ)-1)=0 ?
The general solution for (cot(θ)-1)(csc(θ)-1)=0 is θ= pi/4+pin,θ= pi/2+2pin