What is the general solution for 2tan^2(θ)-5tan(θ)+4=-8tan(θ)+6 ?

The general solution for 2tan^2(θ)-5tan(θ)+4=-8tan(θ)+6 is θ=0.46364…+pin,θ=-1.10714…+pin

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2tan^2(θ)-5tan(θ)+4=-8tan(θ)+6

2 tan^{2} (θ) - 5 tan (θ) + 4 = - 8 tan (θ) + 6

θ = 0.46364 \dots + πn, θ = - 1.10714 \dots + πn

Solution steps

2 tan^{2} (θ) - 5 tan (θ) + 4 = - 8 tan (θ) + 6

Solve by substitution

tan (θ) = \frac{1}{2}, tan (θ) = - 2

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

tan (θ) = - 2 : θ = arctan (- 2) + πn

Combine all the solutions

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

Show solutions in decimal form

θ = 0.46364 \dots + πn, θ = - 1.10714 \dots + πn

1 + \frac{tan ^{2} ( θ )}{sec ( θ )} = sec (θ)

170 = \frac{16 0 ^{2}}{32} sin (2 θ)

sin (3 x) = 3 sin (x) cos (x)

sin (x) = \frac{2 π}{5}

sin (x) = \frac{2 π}{7}

What is the general solution for 2tan^2(θ)-5tan(θ)+4=-8tan(θ)+6 ?
The general solution for 2tan^2(θ)-5tan(θ)+4=-8tan(θ)+6 is θ=0.46364…+pin,θ=-1.10714…+pin