What is the general solution for 10=6.7+13.75tan(θ)-4.718(1+tan^2(θ)) ?

The general solution for 10=6.7+13.75tan(θ)-4.718(1+tan^2(θ)) is θ=0.67843…+pin,θ=1.12790…+pin

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10=6.7+13.75tan(θ)-4.718(1+tan^2(θ))

10 = 6.7 + 13.75 tan (θ) - 4.718 (1 + tan^{2} (θ))

θ = 0.67843 \dots + πn, θ = 1.12790 \dots + πn

Solution steps

10 = 6.7 + 13.75 tan (θ) - 4.718 (1 + tan^{2} (θ))

Switch sides

6.7 + 13.75 tan (θ) - 4.718 (1 + tan^{2} (θ)) = 10

Solve by substitution

tan (θ) = \frac{6875 - 9436701}{4718}, tan (θ) = \frac{6875 + 9436701}{4718}

tan (θ) = \frac{6875 - 9436701}{4718} : θ = arctan (\frac{6875 - 9436701}{4718}) + πn

tan (θ) = \frac{6875 + 9436701}{4718} : θ = arctan (\frac{6875 + 9436701}{4718}) + πn

Combine all the solutions

θ = arctan (\frac{6875 - 9436701}{4718}) + πn, θ = arctan (\frac{6875 + 9436701}{4718}) + πn

Show solutions in decimal form

θ = 0.67843 \dots + πn, θ = 1.12790 \dots + πn

2 cos (3 θ) = - 3

cos (θ) = - cos (θ)

cot (x) cos (x) = cos (x)

tan^{4} (θ) - 20 tan^{2} (θ) + 64 = 0

sin (2 t) = - cos (2 t)

What is the general solution for 10=6.7+13.75tan(θ)-4.718(1+tan^2(θ)) ?
The general solution for 10=6.7+13.75tan(θ)-4.718(1+tan^2(θ)) is θ=0.67843…+pin,θ=1.12790…+pin