What is the general solution for 3tan^2(θ)-1=0 ?

The general solution for 3tan^2(θ)-1=0 is θ=0.52359…+pin,θ=-0.52359…+pin

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3tan^2(θ)-1=0

3 tan^{2} (θ) - 1 = 0

θ = 0.52359 \dots + πn, θ = - 0.52359 \dots + πn

Solution steps

3 tan^{2} (θ) - 1 = 0

Solve by substitution

tan (θ) = \frac{1}{3}, tan (θ) = - \frac{1}{3}

tan (θ) = \frac{1}{3} : θ = arctan (\frac{1}{3}) + πn

tan (θ) = - \frac{1}{3} : θ = arctan (- \frac{1}{3}) + πn

Combine all the solutions

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

Show solutions in decimal form

θ = 0.52359 \dots + πn, θ = - 0.52359 \dots + πn

sin (2 θ - \frac{π}{2}) = - 1

sin (\frac{x}{2}) + cos (x) = 0

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

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

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

What is the general solution for 3tan^2(θ)-1=0 ?
The general solution for 3tan^2(θ)-1=0 is θ=0.52359…+pin,θ=-0.52359…+pin