What is the general solution for 3tan(θ)sin(θ)-2tan(θ)=0 ?

The general solution for 3tan(θ)sin(θ)-2tan(θ)=0 is θ=pin,θ=0.72972…+2pin,θ=pi-0.72972…+2pin

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3tan(θ)sin(θ)-2tan(θ)=0

3 tan (θ) sin (θ) - 2 tan (θ) = 0

θ = πn, θ = 0.72972 \dots + 2 πn, θ = π - 0.72972 \dots + 2 πn

Solution steps

3 tan (θ) sin (θ) - 2 tan (θ) = 0

Factor

3 tan (θ) sin (θ) - 2 tan (θ) : tan (θ) (3 sin (θ) - 2)

tan (θ) (3 sin (θ) - 2) = 0

Solving each part separately

tan (θ) = 0 or 3 sin (θ) - 2 = 0

tan (θ) = 0 : θ = πn

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

Combine all the solutions

θ = πn, θ = arcsin (\frac{2}{3}) + 2 πn, θ = π - arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

θ = πn, θ = 0.72972 \dots + 2 πn, θ = π - 0.72972 \dots + 2 πn

- 8 csc^{2} (x) + 2 cot (x) = - 23

- 6 sin (2 x) = 32

3 cot (2 x) + 1 = 0

sin (4 t) = 0

5 sec (θ) - 3 = 2

What is the general solution for 3tan(θ)sin(θ)-2tan(θ)=0 ?
The general solution for 3tan(θ)sin(θ)-2tan(θ)=0 is θ=pin,θ=0.72972…+2pin,θ=pi-0.72972…+2pin