What is the general solution for 7tan(x)=2sqrt(3)+tan(x) ?

The general solution for 7tan(x)=2sqrt(3)+tan(x) is x= pi/6+pin

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7tan(x)=2sqrt(3)+tan(x)

7 tan (x) = 23 + tan (x)

x = \frac{π}{6} + πn

Degrees

x = 3 0^{\circ} + 18 0^{\circ} n

Solution steps

7 tan (x) = 23 + tan (x)

Solve by substitution

7 tan (x) = 23 + tan (x)

Let:

tan (x) = u

7 u = 23 + u

7 u = 23 + u : u = \frac{3}{3}

7 u = 23 + u

Move

u

to the left side

7 u = 23 + u

Subtract

u

from both sides

7 u - u = 23 + u - u

Simplify

6 u = 23

6 u = 23

Divide both sides by

6

6 u = 23

Divide both sides by

6

\frac{6 u}{6} = \frac{2 3}{6}

Simplify

u = \frac{3}{3}

u = \frac{3}{3}

Substitute back

u = tan (x)

tan (x) = \frac{3}{3}

tan (x) = \frac{3}{3}

tan (x) = \frac{3}{3} : x = \frac{π}{6} + πn

tan (x) = \frac{3}{3}

General solutions for

tan (x) = \frac{3}{3}

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}

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

Combine all the solutions

x = \frac{π}{6} + πn

sin (θ) - 3 cos (θ) = 0

- 3 sin (x) + cos^{2} (x) = 3

sin (x) cos (x) cos (2 x) = \frac{1}{8}

1 + sin (θ) = cos (θ)

sec (x) = 4 cos (x)

What is the general solution for 7tan(x)=2sqrt(3)+tan(x) ?
The general solution for 7tan(x)=2sqrt(3)+tan(x) is x= pi/6+pin