What is the general solution for sin(θ)cot^2(θ)-3sin(θ)=0 ?

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

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sin(θ)cot^2(θ)-3sin(θ)=0

sin (θ) cot^{2} (θ) - 3 sin (θ) = 0

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

Solution steps

sin (θ) cot^{2} (θ) - 3 sin (θ) = 0

Factor

sin (θ) cot^{2} (θ) - 3 sin (θ) : sin (θ) (cot (θ) + 3) (cot (θ) - 3)

sin (θ) (cot (θ) + 3) (cot (θ) - 3) = 0

Solving each part separately

sin (θ) = 0 or cot (θ) + 3 = 0 or cot (θ) - 3 = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

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

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

Combine all the solutions

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

Since the equation is undefined for:

2 πn, π + 2 πn

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

- 6 sin (x) - 3 = 9

5 sin^{2} (x) + cos^{2} (x) = 2

cos (θ) = - \frac{3}{7}

tan (x) cos (x) = \frac{1}{2}

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

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