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

Degrees

θ = 57.99461 \dots^{\circ} + 18 0^{\circ} n

Solution steps

- 2 tan (θ) + 1 = 3 tan (θ) - 7

Solve by substitution

- 2 tan (θ) + 1 = 3 tan (θ) - 7

Let:

tan (θ) = u

- 2 u + 1 = 3 u - 7

- 2 u + 1 = 3 u - 7 : u = \frac{8}{5}

- 2 u + 1 = 3 u - 7

Move

1

to the right side

- 2 u + 1 = 3 u - 7

Subtract

1

from both sides

- 2 u + 1 - 1 = 3 u - 7 - 1

Simplify

- 2 u = 3 u - 8

- 2 u = 3 u - 8

Move

3 u

to the left side

- 2 u = 3 u - 8

Subtract

3 u

from both sides

- 2 u - 3 u = 3 u - 8 - 3 u

Simplify

- 5 u = - 8

- 5 u = - 8

Divide both sides by

- 5

- 5 u = - 8

Divide both sides by

- 5

\frac{- 5 u}{- 5} = \frac{- 8}{- 5}

Simplify

u = \frac{8}{5}

u = \frac{8}{5}

Substitute back

u = tan (θ)

tan (θ) = \frac{8}{5}

tan (θ) = \frac{8}{5}

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

tan (θ) = \frac{8}{5}

Apply trig inverse properties

tan (θ) = \frac{8}{5}

General solutions for

tan (θ) = \frac{8}{5}

tan (x) = a \Rightarrow x = arctan (a) + πn

θ = arctan (\frac{8}{5}) + πn

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