What is the general solution for 4tan^2(θ)=11tan(θ)+3 ?

The general solution for 4tan^2(θ)=11tan(θ)+3 is θ=1.24904…+pin,θ=-0.24497…+pin

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4tan^2(θ)=11tan(θ)+3

4 tan^{2} (θ) = 11 tan (θ) + 3

θ = 1.24904 \dots + πn, θ = - 0.24497 \dots + πn

Solution steps

4 tan^{2} (θ) = 11 tan (θ) + 3

Solve by substitution

tan (θ) = 3, tan (θ) = - \frac{1}{4}

tan (θ) = 3 : θ = arctan (3) + πn

tan (θ) = - \frac{1}{4} : θ = arctan (- \frac{1}{4}) + πn

Combine all the solutions

θ = arctan (3) + πn, θ = arctan (- \frac{1}{4}) + πn

Show solutions in decimal form

θ = 1.24904 \dots + πn, θ = - 0.24497 \dots + πn

6 tan^{2} (x) - 2 cos^{2} (x) = cos (2 x)

2 cos^{2} (x) - 3 sin (x) - 3 = 0

6 tan (θ) + 5 = 0

x, y = arcsin (x)

tan (a) = \frac{5}{12}

What is the general solution for 4tan^2(θ)=11tan(θ)+3 ?
The general solution for 4tan^2(θ)=11tan(θ)+3 is θ=1.24904…+pin,θ=-0.24497…+pin