What is the general solution for 8tan^2(θ)-1=3tan(θ)+4 ?

The general solution for 8tan^2(θ)-1=3tan(θ)+4 is θ= pi/4+pin,θ=-0.55859…+pin

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8tan^2(θ)-1=3tan(θ)+4

8 tan^{2} (θ) - 1 = 3 tan (θ) + 4

θ = \frac{π}{4} + πn, θ = - 0.55859 \dots + πn

Solution steps

8 tan^{2} (θ) - 1 = 3 tan (θ) + 4

Solve by substitution

tan (θ) = 1, tan (θ) = - \frac{5}{8}

tan (θ) = 1 : θ = \frac{π}{4} + πn

tan (θ) = - \frac{5}{8} : θ = arctan (- \frac{5}{8}) + πn

Combine all the solutions

θ = \frac{π}{4} + πn, θ = arctan (- \frac{5}{8}) + πn

Show solutions in decimal form

θ = \frac{π}{4} + πn, θ = - 0.55859 \dots + πn

2 csc^{2} (x) + csc (x) - 2 = 0

2 sin (A) - 1 = 0

cos (5 θ) = cos (3 θ)

cos (x 1) - cos (x 2) = cos (x 1 - x 2)

8 \cdot sin^{2} (2 x) - 2 \cdot sin (2 x) - 1 = 0

What is the general solution for 8tan^2(θ)-1=3tan(θ)+4 ?
The general solution for 8tan^2(θ)-1=3tan(θ)+4 is θ= pi/4+pin,θ=-0.55859…+pin