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

The general solution for (csc(θ)-2)(cot(θ)+1)=0 is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ=(3pi)/4+pin

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(csc(θ)-2)(cot(θ)+1)=0

(csc (θ) - 2) (cot (θ) + 1) = 0

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = \frac{3 π}{4} + πn

Solution steps

(csc (θ) - 2) (cot (θ) + 1) = 0

Solving each part separately

csc (θ) - 2 = 0 or cot (θ) + 1 = 0

csc (θ) - 2 = 0 : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

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

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = \frac{3 π}{4} + πn

sin (x) = csc (x)

9 sin (x) tan (x) = 10 tan (x)

3 sin^{2} (θ) + 6 = 2 sin^{2} (θ) + 7

10 sin^{2} (4 x) = 5

cosh (x) = 2

What is the general solution for (csc(θ)-2)(cot(θ)+1)=0 ?
The general solution for (csc(θ)-2)(cot(θ)+1)=0 is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ=(3pi)/4+pin