What is the general solution for sin(θ)tan(θ)-sqrt(3)sin(θ)=0 ?

The general solution for sin(θ)tan(θ)-sqrt(3)sin(θ)=0 is θ=2pin,θ=pi+2pin,θ= pi/3+pin

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sin(θ)tan(θ)-sqrt(3)sin(θ)=0

sin (θ) tan (θ) - 3 sin (θ) = 0

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

Solution steps

sin (θ) tan (θ) - 3 sin (θ) = 0

Factor

sin (θ) tan (θ) - 3 sin (θ) : sin (θ) (tan (θ) - 3)

sin (θ) (tan (θ) - 3) = 0

Solving each part separately

sin (θ) = 0 or tan (θ) - 3 = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

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

Combine all the solutions

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

53 tan (x) - 5 = 0

x, y = arctan (x + 1)

2 cos (2 θ) + 4 cos (θ) + 2 = - 1

2 cos (2 x + \frac{3 π}{2}) = 3

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

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