What is the general solution for sqrt(3)csc(θ)+csc(θ)cot(θ)=0 ?

The general solution for sqrt(3)csc(θ)+csc(θ)cot(θ)=0 is θ=(5pi)/6+pin

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sqrt(3)csc(θ)+csc(θ)cot(θ)=0

3 csc (θ) + csc (θ) cot (θ) = 0

θ = \frac{5 π}{6} + πn

Solution steps

3 csc (θ) + csc (θ) cot (θ) = 0

Factor

3 csc (θ) + csc (θ) cot (θ) : csc (θ) (3 + cot (θ))

csc (θ) (3 + cot (θ)) = 0

Solving each part separately

csc (θ) = 0 or 3 + cot (θ) = 0

csc (θ) = 0 :

No Solution

3 + cot (θ) = 0 : θ = \frac{5 π}{6} + πn

Combine all the solutions

θ = \frac{5 π}{6} + πn

tan (x) (cot (x) + 1) = 0

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

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

csc^{2} (x) = 9

csc^{2} (x) = 3

What is the general solution for sqrt(3)csc(θ)+csc(θ)cot(θ)=0 ?
The general solution for sqrt(3)csc(θ)+csc(θ)cot(θ)=0 is θ=(5pi)/6+pin