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

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

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2cos(θ)tan(θ)-tan(θ)=0

2 cos (θ) tan (θ) - tan (θ) = 0

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

Solution steps

2 cos (θ) tan (θ) - tan (θ) = 0

Factor

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

tan (θ) (2 cos (θ) - 1) = 0

Solving each part separately

tan (θ) = 0 or 2 cos (θ) - 1 = 0

tan (θ) = 0 : θ = πn

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

Combine all the solutions

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

3 csc (x) = 2, 3 csc (x) = 2

3 csc (x) + 2 = 4

2 = csc (θ)

cos^{2} (15 0^{\circ}) - sin^{2} (15 0^{\circ}) = tan (x)

3 - sin (x) = 0

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