What is the general solution for -4tan(θ)-10=4tan(θ)-7 ?

The general solution for -4tan(θ)-10=4tan(θ)-7 is θ=-0.35877…+pin

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-4tan(θ)-10=4tan(θ)-7

- 4 tan (θ) - 10 = 4 tan (θ) - 7

θ = - 0.35877 \dots + πn

Degrees

θ = - 20.55604 \dots^{\circ} + 18 0^{\circ} n

Solution steps

- 4 tan (θ) - 10 = 4 tan (θ) - 7

Solve by substitution

- 4 tan (θ) - 10 = 4 tan (θ) - 7

Let:

tan (θ) = u

- 4 u - 10 = 4 u - 7

- 4 u - 10 = 4 u - 7 : u = - \frac{3}{8}

- 4 u - 10 = 4 u - 7

Move

10

to the right side

- 4 u - 10 = 4 u - 7

Add

10

to both sides

- 4 u - 10 + 10 = 4 u - 7 + 10

Simplify

- 4 u = 4 u + 3

- 4 u = 4 u + 3

Move

4 u

to the left side

- 4 u = 4 u + 3

Subtract

4 u

from both sides

- 4 u - 4 u = 4 u + 3 - 4 u

Simplify

- 8 u = 3

- 8 u = 3

Divide both sides by

- 8

- 8 u = 3

Divide both sides by

- 8

\frac{- 8 u}{- 8} = \frac{3}{- 8}

Simplify

u = - \frac{3}{8}

u = - \frac{3}{8}

Substitute back

u = tan (θ)

tan (θ) = - \frac{3}{8}

tan (θ) = - \frac{3}{8}

tan (θ) = - \frac{3}{8} : θ = arctan (- \frac{3}{8}) + πn

tan (θ) = - \frac{3}{8}

Apply trig inverse properties

tan (θ) = - \frac{3}{8}

General solutions for

tan (θ) = - \frac{3}{8}

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

θ = arctan (- \frac{3}{8}) + πn

θ = arctan (- \frac{3}{8}) + πn

Combine all the solutions

θ = arctan (- \frac{3}{8}) + πn

Show solutions in decimal form

θ = - 0.35877 \dots + πn

sin (x) = sin (x^{2})

sin (x) = - 0.23

2 sin^{2} (x) + 3 sin (x) + 1 = 0, 0 \leq x \leq 2 π

cos (3 x) - 1 = sin (3 x)

sin (\frac{x}{3}) = \frac{2}{2}

What is the general solution for -4tan(θ)-10=4tan(θ)-7 ?
The general solution for -4tan(θ)-10=4tan(θ)-7 is θ=-0.35877…+pin