What is the general solution for 3tan^2(θ)+7tan(θ)-2=4 ?

The general solution for 3tan^2(θ)+7tan(θ)-2=4 is θ=0.58800…+pin,θ=-1.24904…+pin

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3tan^2(θ)+7tan(θ)-2=4

3 tan^{2} (θ) + 7 tan (θ) - 2 = 4

θ = 0.58800 \dots + πn, θ = - 1.24904 \dots + πn

Solution steps

3 tan^{2} (θ) + 7 tan (θ) - 2 = 4

Solve by substitution

tan (θ) = \frac{2}{3}, tan (θ) = - 3

tan (θ) = \frac{2}{3} : θ = arctan (\frac{2}{3}) + πn

tan (θ) = - 3 : θ = arctan (- 3) + πn

Combine all the solutions

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

Show solutions in decimal form

θ = 0.58800 \dots + πn, θ = - 1.24904 \dots + πn

4 sin^{2} (x) = 0

5 cos (2 θ) = - 5 cos (θ)

sin (θ) = \frac{3}{5}, 0 < θ < \frac{π}{2}

cos (4 x) cos (x) + sin (4 x) sin (x) = \frac{1}{2}

- 4 sin^{2} (θ) - 15 sin (θ) = - 7 sin (θ) - 5

What is the general solution for 3tan^2(θ)+7tan(θ)-2=4 ?
The general solution for 3tan^2(θ)+7tan(θ)-2=4 is θ=0.58800…+pin,θ=-1.24904…+pin