What is the general solution for 5sin(θ)tan(θ)-10tan(θ)+3sin(θ)-6=0 ?

The general solution for 5sin(θ)tan(θ)-10tan(θ)+3sin(θ)-6=0 is θ=-0.54041…+pin

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5sin(θ)tan(θ)-10tan(θ)+3sin(θ)-6=0

5 sin (θ) tan (θ) - 10 tan (θ) + 3 sin (θ) - 6 = 0

θ = - 0.54041 \dots + πn

Solution steps

5 sin (θ) tan (θ) - 10 tan (θ) + 3 sin (θ) - 6 = 0

Factor

5 sin (θ) tan (θ) - 10 tan (θ) + 3 sin (θ) - 6 : (sin (θ) - 2) (5 tan (θ) + 3)

(sin (θ) - 2) (5 tan (θ) + 3) = 0

Solving each part separately

sin (θ) - 2 = 0 or 5 tan (θ) + 3 = 0

sin (θ) - 2 = 0 :

No Solution

5 tan (θ) + 3 = 0 : θ = arctan (- \frac{3}{5}) + πn

Combine all the solutions

θ = arctan (- \frac{3}{5}) + πn

Show solutions in decimal form

θ = - 0.54041 \dots + πn

3 cos^{2} (θ) + 6 cos (θ) - 4 = 0

arccos (x) = 1

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

sin (x) = sin (\frac{x}{2})

sec (x) - 2 = - tan (x) - 3

What is the general solution for 5sin(θ)tan(θ)-10tan(θ)+3sin(θ)-6=0 ?
The general solution for 5sin(θ)tan(θ)-10tan(θ)+3sin(θ)-6=0 is θ=-0.54041…+pin