What is the general solution for 9tan^2(θ)-4=0 ?

The general solution for 9tan^2(θ)-4=0 is θ=0.58800…+pin,θ=-0.58800…+pin

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9tan^2(θ)-4=0

9 tan^{2} (θ) - 4 = 0

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

Solution steps

9 tan^{2} (θ) - 4 = 0

Solve by substitution

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

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

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

Combine all the solutions

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

Show solutions in decimal form

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

cos (x) = 1 + sin (x)

cot (x - \frac{π}{4}) = - 1

3 cos (θ) + 1 = 1

sin (θ) = 3

2 cos (x) csc (x) = 2 cos (x)

What is the general solution for 9tan^2(θ)-4=0 ?
The general solution for 9tan^2(θ)-4=0 is θ=0.58800…+pin,θ=-0.58800…+pin