What is the general solution for sqrt(3)tan(x)-2=-1 ?

The general solution for sqrt(3)tan(x)-2=-1 is x= pi/6+pin

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sqrt(3)tan(x)-2=-1

3 tan (x) - 2 = - 1

x = \frac{π}{6} + πn

Degrees

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

Solution steps

3 tan (x) - 2 = - 1

Move

2

to the right side

3 tan (x) - 2 = - 1

Add

2

to both sides

3 tan (x) - 2 + 2 = - 1 + 2

Simplify

3 tan (x) = 1

3 tan (x) = 1

Divide both sides by

3

3 tan (x) = 1

Divide both sides by

3

\frac{3 tan ( x )}{3} = \frac{1}{3}

Simplify

\frac{3 tan ( x )}{3} = \frac{1}{3}

Simplify

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

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

Cancel the common factor:

3

= tan (x)

Simplify

\frac{1}{3} : \frac{3}{3}

\frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{3}{3}

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

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

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

x, 1 - cos (x) = 0

sin (a) = \frac{- 3}{2}

sin (x) = 467

csc (x) = \frac{5}{3}

sin (B) = \frac{( 240.68 \cdot sin ( 21.1 6 ^{\circ} ) )}{207.91}

What is the general solution for sqrt(3)tan(x)-2=-1 ?
The general solution for sqrt(3)tan(x)-2=-1 is x= pi/6+pin