What is the general solution for 11tan(θ)-10=4tan(θ)-4 ?

The general solution for 11tan(θ)-10=4tan(θ)-4 is θ=0.70862…+pin

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11tan(θ)-10=4tan(θ)-4

11 tan (θ) - 10 = 4 tan (θ) - 4

θ = 0.70862 \dots + πn

Degrees

θ = 40.60129 \dots^{\circ} + 18 0^{\circ} n

Solution steps

11 tan (θ) - 10 = 4 tan (θ) - 4

Solve by substitution

11 tan (θ) - 10 = 4 tan (θ) - 4

Let:

tan (θ) = u

11 u - 10 = 4 u - 4

11 u - 10 = 4 u - 4 : u = \frac{6}{7}

11 u - 10 = 4 u - 4

Move

10

to the right side

11 u - 10 = 4 u - 4

Add

10

to both sides

11 u - 10 + 10 = 4 u - 4 + 10

Simplify

11 u = 4 u + 6

11 u = 4 u + 6

Move

4 u

to the left side

11 u = 4 u + 6

Subtract

4 u

from both sides

11 u - 4 u = 4 u + 6 - 4 u

Simplify

7 u = 6

7 u = 6

Divide both sides by

7

7 u = 6

Divide both sides by

7

\frac{7 u}{7} = \frac{6}{7}

Simplify

u = \frac{6}{7}

u = \frac{6}{7}

Substitute back

u = tan (θ)

tan (θ) = \frac{6}{7}

tan (θ) = \frac{6}{7}

tan (θ) = \frac{6}{7} : θ = arctan (\frac{6}{7}) + πn

tan (θ) = \frac{6}{7}

Apply trig inverse properties

tan (θ) = \frac{6}{7}

General solutions for

tan (θ) = \frac{6}{7}

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

θ = arctan (\frac{6}{7}) + πn

θ = arctan (\frac{6}{7}) + πn

Combine all the solutions

θ = arctan (\frac{6}{7}) + πn

Show solutions in decimal form

θ = 0.70862 \dots + πn

sec^{2} (x) - 8 sec (x) = 0

cot^{2} (x) = 1 + csc (x)

7 tan (A) + 42 = 0

2 sin (x + \frac{π}{4}) = 1

cos (3 x) = \frac{1}{2}

What is the general solution for 11tan(θ)-10=4tan(θ)-4 ?
The general solution for 11tan(θ)-10=4tan(θ)-4 is θ=0.70862…+pin