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

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

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sin(θ)cos(θ)=sin(θ)

sin (θ) cos (θ) = sin (θ)

θ = 2 πn, θ = π + 2 πn

Solution steps

sin (θ) cos (θ) = sin (θ)

Subtract

sin (θ)

from both sides

sin (θ) cos (θ) - sin (θ) = 0

Factor

sin (θ) cos (θ) - sin (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 = 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn

7 cos (x) + 4 = - cos (x)

2 sin^{2} (θ) - sin (θ) - 1 = 0, 0 \leq θ < 2 π

3 sin (x) = tan (x)

cos^{2} (θ) + cos (θ) = sin^{2} (θ)

cos (4 x) = \frac{3}{2}

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