What is the general solution for 25tan^2(θ)-4=0 ?

The general solution for 25tan^2(θ)-4=0 is θ=0.38050…+pin,θ=-0.38050…+pin

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25tan^2(θ)-4=0

25 tan^{2} (θ) - 4 = 0

θ = 0.38050 \dots + πn, θ = - 0.38050 \dots + πn

Solution steps

25 tan^{2} (θ) - 4 = 0

Solve by substitution

tan (θ) = \frac{2}{5}, tan (θ) = - \frac{2}{5}

tan (θ) = \frac{2}{5} : θ = arctan (\frac{2}{5}) + πn

tan (θ) = - \frac{2}{5} : θ = arctan (- \frac{2}{5}) + πn

Combine all the solutions

θ = arctan (\frac{2}{5}) + πn, θ = arctan (- \frac{2}{5}) + πn

Show solutions in decimal form

θ = 0.38050 \dots + πn, θ = - 0.38050 \dots + πn

tan (x) = \frac{8}{15}

sin (θ) = - \frac{12}{13}

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

sec^{2} (θ) - 9 = 0

2 cos^{2} (θ) = 2 - sin (θ)

What is the general solution for 25tan^2(θ)-4=0 ?
The general solution for 25tan^2(θ)-4=0 is θ=0.38050…+pin,θ=-0.38050…+pin