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

The general solution for (cot(θ)+1)(sin(θ)-1)=0 is θ=(3pi)/4+pin,θ= pi/2+2pin

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(cot(θ)+1)(sin(θ)-1)=0

(cot (θ) + 1) (sin (θ) - 1) = 0

θ = \frac{3 π}{4} + πn, θ = \frac{π}{2} + 2 πn

Solution steps

(cot (θ) + 1) (sin (θ) - 1) = 0

Solving each part separately

cot (θ) + 1 = 0 or sin (θ) - 1 = 0

cot (θ) + 1 = 0 : θ = \frac{3 π}{4} + πn

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

Combine all the solutions

θ = \frac{3 π}{4} + πn, θ = \frac{π}{2} + 2 πn

sec (2 x) = tan (2 x) + 1

sec^{2} (x) + 3 sec (x) + 2 = 0

3 sin (x) cos (x) - 2 cos (x) = 0

sin (x) = cos (x) + 1

5 sin (x) + 2 = 0

What is the general solution for (cot(θ)+1)(sin(θ)-1)=0 ?
The general solution for (cot(θ)+1)(sin(θ)-1)=0 is θ=(3pi)/4+pin,θ= pi/2+2pin