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

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

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sin(θ)cos(θ)=cos(θ)

sin (θ) cos (θ) = cos (θ)

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

Solution steps

sin (θ) cos (θ) = cos (θ)

Subtract

cos (θ)

from both sides

sin (θ) cos (θ) - cos (θ) = 0

Factor

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

cos (θ) (sin (θ) - 1) = 0

Solving each part separately

cos (θ) = 0 or sin (θ) - 1 = 0

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

sin (θ) - 1 = 0 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

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

tan^{2} (2 θ) = 3

tan^{2} (2 θ) = 1

(50.691) cos (50.69 1^{\circ} - c) + sin (50.69 1^{\circ} - c) = 0

sec (4 θ) = 2

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

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