What is the general solution for sin(θ)-2sin(θ)cos(θ)=0 ?

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

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sin(θ)-2sin(θ)cos(θ)=0

sin (θ) - 2 sin (θ) cos (θ) = 0

θ = 2 πn, θ = π + 2 πn, θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

sin (θ) - 2 sin (θ) cos (θ) = 0

Factor

sin (θ) - 2 sin (θ) cos (θ) : - sin (θ) (2 cos (θ) - 1)

- sin (θ) (2 cos (θ) - 1) = 0

Solving each part separately

sin (θ) = 0 or 2 cos (θ) - 1 = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

2 cos (θ) - 1 = 0 : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn, θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

6 cos^{2} (x) + cos (2 x) = 1

sin (2 π t) = 1

(4 cos^{2} (x) - 3) (csc (x) + 2) = 0

sin (x) = cos (2 x + 10)

sin (x) + 2 sin^{2} (x) = 1

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