What is the general solution for sin(θ)=-sin(θ)cos(θ) ?

The general solution for sin(θ)=-sin(θ)cos(θ) is θ=2pin,θ=pi+2pin

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sin(θ)=-sin(θ)cos(θ)

sin (θ) = - sin (θ) cos (θ)

θ = 2 πn, θ = π + 2 πn

Solution steps

sin (θ) = - sin (θ) cos (θ)

Subtract

- sin (θ) cos (θ)

from both sides

sin (θ) + sin (θ) cos (θ) = 0

Factor

sin (θ) + sin (θ) cos (θ) : sin (θ) (cos (θ) + 1)

sin (θ) (cos (θ) + 1) = 0

Solving each part separately

sin (θ) = 0 or cos (θ) + 1 = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

cos (θ) + 1 = 0 : θ = π + 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn

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

sin (x) = \frac{2}{25}

4 + tan (x) = 5 cot (x)

3 (sin (x) - 2) (4 cos (x) - 2) = 0

\frac{sin ( x )}{120} = \frac{sin ( 8 )}{30}

What is the general solution for sin(θ)=-sin(θ)cos(θ) ?
The general solution for sin(θ)=-sin(θ)cos(θ) is θ=2pin,θ=pi+2pin