What is the general solution for -2tan^2(θ)-4tan(θ)+2=3tan(θ)+5 ?

The general solution for -2tan^2(θ)-4tan(θ)+2=3tan(θ)+5 is θ=-1.24904…+pin,θ=-0.46364…+pin

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-2tan^2(θ)-4tan(θ)+2=3tan(θ)+5

- 2 tan^{2} (θ) - 4 tan (θ) + 2 = 3 tan (θ) + 5

θ = - 1.24904 \dots + πn, θ = - 0.46364 \dots + πn

Solution steps

- 2 tan^{2} (θ) - 4 tan (θ) + 2 = 3 tan (θ) + 5

Solve by substitution

tan (θ) = - 3, tan (θ) = - \frac{1}{2}

tan (θ) = - 3 : θ = arctan (- 3) + πn

tan (θ) = - \frac{1}{2} : θ = arctan (- \frac{1}{2}) + πn

Combine all the solutions

θ = arctan (- 3) + πn, θ = arctan (- \frac{1}{2}) + πn

Show solutions in decimal form

θ = - 1.24904 \dots + πn, θ = - 0.46364 \dots + πn

csc (3 x) = 1

x, cos (x + y) + cos (x) = 0

cos (\frac{π t}{2}) \frac{π}{2} = 0

sin (x) + 2 cos (x) = 0

sec^{2} (x) + csc^{2} (x) = 1

What is the general solution for -2tan^2(θ)-4tan(θ)+2=3tan(θ)+5 ?
The general solution for -2tan^2(θ)-4tan(θ)+2=3tan(θ)+5 is θ=-1.24904…+pin,θ=-0.46364…+pin