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

The general solution for tan(θ)sin(θ)+sin(θ)=0 is θ=2pin,θ=pi+2pin,θ=(3pi)/4+pin

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tan(θ)sin(θ)+sin(θ)=0

tan (θ) sin (θ) + sin (θ) = 0

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

Solution steps

tan (θ) sin (θ) + sin (θ) = 0

Factor

tan (θ) sin (θ) + sin (θ) : sin (θ) (tan (θ) + 1)

sin (θ) (tan (θ) + 1) = 0

Solving each part separately

sin (θ) = 0 or tan (θ) + 1 = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

tan (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

tan (x) = 0.5

3 sin (x) = cos (x)

sec^{2} (x) - 3 sec (x) = 0

3 cot (x) + 1 = 0

tan (x) = - \frac{2}{3}

What is the general solution for tan(θ)sin(θ)+sin(θ)=0 ?
The general solution for tan(θ)sin(θ)+sin(θ)=0 is θ=2pin,θ=pi+2pin,θ=(3pi)/4+pin