What is the general solution for 5sqrt(3)tan(x)-5=0 ?

The general solution for 5sqrt(3)tan(x)-5=0 is x= pi/6+pin

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5sqrt(3)tan(x)-5=0

53 tan (x) - 5 = 0

x = \frac{π}{6} + πn

Degrees

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

Solution steps

53 tan (x) - 5 = 0

Move

5

to the right side

53 tan (x) - 5 = 0

Add

5

to both sides

53 tan (x) - 5 + 5 = 0 + 5

Simplify

53 tan (x) = 5

53 tan (x) = 5

Divide both sides by

53

53 tan (x) = 5

Divide both sides by

53

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

Simplify

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

Simplify

\frac{5 3 tan ( x )}{5 3} : tan (x)

\frac{5 3 tan ( x )}{5 3}

Divide the numbers:

\frac{5}{5} = 1

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

Cancel the common factor:

3

= tan (x)

Simplify

\frac{5}{5 3} : \frac{3}{3}

\frac{5}{5 3}

Divide the numbers:

\frac{5}{5} = 1

= \frac{1}{3}

Rationalize

\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}

= \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, y = arctan (x + 1)

2 cos (2 θ) + 4 cos (θ) + 2 = - 1

2 cos (2 x + \frac{3 π}{2}) = 3

3 sin (x) + 2 cos (x) = 0

2 = sec^{2} (x)

What is the general solution for 5sqrt(3)tan(x)-5=0 ?
The general solution for 5sqrt(3)tan(x)-5=0 is x= pi/6+pin