What is the general solution for 8tan(θ)-12=5tan(θ)-9 ?

The general solution for 8tan(θ)-12=5tan(θ)-9 is θ= pi/4+pin

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Popular Trigonometry >

8tan(θ)-12=5tan(θ)-9

Solution

8 tan (θ) - 12 = 5 tan (θ) - 9

Solution

θ = \frac{π}{4} + πn

Degrees

θ = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

8 tan (θ) - 12 = 5 tan (θ) - 9

Solve by substitution

8 tan (θ) - 12 = 5 tan (θ) - 9

Let:

tan (θ) = u

8 u - 12 = 5 u - 9

8 u - 12 = 5 u - 9 : u = 1

8 u - 12 = 5 u - 9

Move

12

to the right side

8 u - 12 = 5 u - 9

Add

12

to both sides

8 u - 12 + 12 = 5 u - 9 + 12

Simplify

8 u = 5 u + 3

8 u = 5 u + 3

Move

5 u

to the left side

8 u = 5 u + 3

Subtract

5 u

from both sides

8 u - 5 u = 5 u + 3 - 5 u

Simplify

3 u = 3

3 u = 3

Divide both sides by

3

3 u = 3

Divide both sides by

3

\frac{3 u}{3} = \frac{3}{3}

Simplify

u = 1

u = 1

Substitute back

u = tan (θ)

tan (θ) = 1

tan (θ) = 1

tan (θ) = 1 : θ = \frac{π}{4} + πn

tan (θ) = 1

General solutions for

tan (θ) = 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

θ = \frac{π}{4} + πn

θ = \frac{π}{4} + πn

Combine all the solutions

θ = \frac{π}{4} + πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 8tan(θ)-12=5tan(θ)-9 ?
The general solution for 8tan(θ)-12=5tan(θ)-9 is θ= pi/4+pin