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

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

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sin(θ)=2sin(θ)cos(θ)

sin (θ) = 2 sin (θ) cos (θ)

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)

Subtract

2 sin (θ) cos (θ)

from both sides

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

x, arccos (e^{- x}) = \frac{π}{3}

2 cos^{2} (4 x + 1) = 0

x, 2 sin (x) = - 1

t, f = a cos (\frac{t π}{6} - \frac{11 π}{12})

- 9 cos^{2} (θ) + 9 = 16 sin (θ) - 7, 0 \leq θ < 36 0^{\circ}

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