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

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

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sin(θ)+sin(θ)cot(θ)=0

sin (θ) + sin (θ) cot (θ) = 0

θ = \frac{3 π}{4} + πn

Solution steps

sin (θ) + sin (θ) cot (θ) = 0

Factor

sin (θ) + sin (θ) cot (θ) : sin (θ) (cot (θ) + 1)

sin (θ) (cot (θ) + 1) = 0

Solving each part separately

sin (θ) = 0 or cot (θ) + 1 = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

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

Combine all the solutions

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

Since the equation is undefined for:

2 πn, π + 2 πn

θ = \frac{3 π}{4} + πn

sin (2 x) = - sin (- x)

cos (x) - 4 = sin (x) - 4

(2 cos (x) + 1) (2 sin (x) + 3) = 0

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

9 cos (x) + 9 sin (x) tan (x) = 18

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