What is the general solution for -2tan(θ)+1=3tan(θ)-7 ?

The general solution for -2tan(θ)+1=3tan(θ)-7 is θ=1.01219…+pin

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-2tan(θ)+1=3tan(θ)-7

- 2 tan (θ) + 1 = 3 tan (θ) - 7

θ = 1.01219 \dots + πn

Solution steps

- 2 tan (θ) + 1 = 3 tan (θ) - 7

Solve by substitution

tan (θ) = \frac{8}{5}

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

Combine all the solutions

θ = arctan (\frac{8}{5}) + πn

Show solutions in decimal form

θ = 1.01219 \dots + πn

5 cos (x) + 2 = 3 cos (x)

- 2 sin^{2} (θ) + 10 sin (θ) - 3 = 3 sin (θ)

cos (2 x) - cos^{2} (x) = 0

tan (π - θ) = tan (θ)

8 cos (x) = sec^{2} (x)

What is the general solution for -2tan(θ)+1=3tan(θ)-7 ?
The general solution for -2tan(θ)+1=3tan(θ)-7 is θ=1.01219…+pin