What is the general solution for -4tan^2(θ)=-1 ?

The general solution for -4tan^2(θ)=-1 is θ=0.46364…+pin,θ=-0.46364…+pin

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-4tan^2(θ)=-1

- 4 tan^{2} (θ) = - 1

θ = 0.46364 \dots + πn, θ = - 0.46364 \dots + πn

Solution steps

- 4 tan^{2} (θ) = - 1

Solve by substitution

tan (θ) = \frac{1}{2}, tan (θ) = - \frac{1}{2}

tan (θ) = \frac{1}{2} : θ = arctan (\frac{1}{2}) + πn

tan (θ) = - \frac{1}{2} : θ = arctan (- \frac{1}{2}) + πn

Combine all the solutions

θ = arctan (\frac{1}{2}) + πn, θ = arctan (- \frac{1}{2}) + πn

Show solutions in decimal form

θ = 0.46364 \dots + πn, θ = - 0.46364 \dots + πn

2 cos^{2} (x) + 5 sin (x) + 1 = 0

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tan (\frac{2 x}{3}) - 3 = 0

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

cos (3 x) \cdot 3 = 0

What is the general solution for -4tan^2(θ)=-1 ?
The general solution for -4tan^2(θ)=-1 is θ=0.46364…+pin,θ=-0.46364…+pin