What is the general solution for sqrt(5)tan(θ)-9=-6tan(θ)+sqrt(8) ?

The general solution for sqrt(5)tan(θ)-9=-6tan(θ)+sqrt(8) is θ=0.96256…+pin

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sqrt(5)tan(θ)-9=-6tan(θ)+sqrt(8)

5 tan (θ) - 9 = - 6 tan (θ) + 8

θ = 0.96256 \dots + πn

Solution steps

5 tan (θ) - 9 = - 6 tan (θ) + 8

Solve by substitution

tan (θ) = - \frac{( 2 2 + 9 ) ( 5 - 6 )}{31}

tan (θ) = - \frac{( 2 2 + 9 ) ( 5 - 6 )}{31} : θ = arctan (- \frac{( 2 2 + 9 ) ( 5 - 6 )}{31}) + πn

Combine all the solutions

θ = arctan (- \frac{( 2 2 + 9 ) ( 5 - 6 )}{31}) + πn

Show solutions in decimal form

θ = 0.96256 \dots + πn

81 (cos^{2} (x)) = 6

(cos (x) - 2) (cos (x) + 1) = 0

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

tan (θ) = \frac{23}{72}

sin (θ - \frac{π}{2}) = cos (θ)

What is the general solution for sqrt(5)tan(θ)-9=-6tan(θ)+sqrt(8) ?
The general solution for sqrt(5)tan(θ)-9=-6tan(θ)+sqrt(8) is θ=0.96256…+pin