What is the general solution for cos(θ)sin(θ)-3cos(θ)=0 ?

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

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cos(θ)sin(θ)-3cos(θ)=0

cos (θ) sin (θ) - 3 cos (θ) = 0

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

Solution steps

cos (θ) sin (θ) - 3 cos (θ) = 0

Factor

cos (θ) sin (θ) - 3 cos (θ) : cos (θ) (sin (θ) - 3)

cos (θ) (sin (θ) - 3) = 0

Solving each part separately

cos (θ) = 0 or sin (θ) - 3 = 0

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

sin (θ) - 3 = 0 :

No Solution

Combine all the solutions

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

\frac{3}{2} = cos (θ)

7 sin (7 x) = 0

csc (θ) = \frac{5}{3}

- 5 sec (x) tan (x) = 0

sin (3 0^{\circ}) = cos (x)

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