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

The general solution for 4tan^2(θ)-25=0 is θ=1.19028…+pin,θ=-1.19028…+pin

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4tan^2(θ)-25=0

4 tan^{2} (θ) - 25 = 0

θ = 1.19028 \dots + πn, θ = - 1.19028 \dots + πn

Solution steps

4 tan^{2} (θ) - 25 = 0

Solve by substitution

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

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

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

Combine all the solutions

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

Show solutions in decimal form

θ = 1.19028 \dots + πn, θ = - 1.19028 \dots + πn

sin^{2} (x) - cos^{2} (x) = - 1

cos^{2} (x) = sin^{2} (x) + 1

4 sin (θ) cos^{2} (θ) = 3 sin (θ)

sin (x) = \frac{7}{25}

cos (x) + 9 sin^{2} (x) = 1

What is the general solution for 4tan^2(θ)-25=0 ?
The general solution for 4tan^2(θ)-25=0 is θ=1.19028…+pin,θ=-1.19028…+pin