What is the general solution for 3tan(θ)-2sqrt(3)=sqrt(3) ?

The general solution for 3tan(θ)-2sqrt(3)=sqrt(3) is θ= pi/3+pin

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3tan(θ)-2sqrt(3)=sqrt(3)

3 tan (θ) - 23 = 3

θ = \frac{π}{3} + πn

Degrees

θ = 6 0^{\circ} + 18 0^{\circ} n

Solution steps

3 tan (θ) - 23 = 3

Move

23

to the right side

3 tan (θ) - 23 = 3

Add

23

to both sides

3 tan (θ) - 23 + 23 = 3 + 23

Simplify

3 tan (θ) - 23 + 23 = 3 + 23

Simplify

3 tan (θ) - 23 + 23 : 3 tan (θ)

3 tan (θ) - 23 + 23

Add similar elements:

- 23 + 23 = 0

= 3 tan (θ)

Simplify

3 + 23 : 33

3 + 23

Add similar elements:

3 + 23 = 33

= 33

3 tan (θ) = 33

3 tan (θ) = 33

3 tan (θ) = 33

Divide both sides by

3

3 tan (θ) = 33

Divide both sides by

3

\frac{3 tan ( θ )}{3} = \frac{3 3}{3}

Simplify

tan (θ) = 3

tan (θ) = 3

General solutions for

tan (θ) = 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}

θ = \frac{π}{3} + πn

θ = \frac{π}{3} + πn

1 - 2 sin^{2} (x) = sin (x)

sin (2 θ) = 2 cos^{2} (θ)

0 = 3 cos (3 θ)

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

tan (2 x - \frac{π}{4}) = - 1

What is the general solution for 3tan(θ)-2sqrt(3)=sqrt(3) ?
The general solution for 3tan(θ)-2sqrt(3)=sqrt(3) is θ= pi/3+pin