What is the general solution for 8tan^2(θ)+10tan(θ)+10=7 ?

The general solution for 8tan^2(θ)+10tan(θ)+10=7 is θ=-0.46364…+pin,θ=-0.64350…+pin

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8tan^2(θ)+10tan(θ)+10=7

8 tan^{2} (θ) + 10 tan (θ) + 10 = 7

θ = - 0.46364 \dots + πn, θ = - 0.64350 \dots + πn

Solution steps

8 tan^{2} (θ) + 10 tan (θ) + 10 = 7

Solve by substitution

tan (θ) = - \frac{1}{2}, tan (θ) = - \frac{3}{4}

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

tan (θ) = - \frac{3}{4} : θ = arctan (- \frac{3}{4}) + πn

Combine all the solutions

θ = arctan (- \frac{1}{2}) + πn, θ = arctan (- \frac{3}{4}) + πn

Show solutions in decimal form

θ = - 0.46364 \dots + πn, θ = - 0.64350 \dots + πn

3 sec (x) - 23 = 0

2 cos (x) - 3 = - 5

sin (3 θ) - sin (θ) = cos (2 θ)

2 sin (x) + (2 - 3) = 3 csc (x)

tan^{2} (θ) + 4 sec (θ) = - 5

What is the general solution for 8tan^2(θ)+10tan(θ)+10=7 ?
The general solution for 8tan^2(θ)+10tan(θ)+10=7 is θ=-0.46364…+pin,θ=-0.64350…+pin