What is the general solution for 3tan(x/2)-sqrt(3)=0 ?

The general solution for 3tan(x/2)-sqrt(3)=0 is x= pi/3+2pin

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3tan(x/2)-sqrt(3)=0

3 tan (\frac{x}{2}) - 3 = 0

x = \frac{π}{3} + 2 πn

Degrees

x = 6 0^{\circ} + 36 0^{\circ} n

Solution steps

3 tan (\frac{x}{2}) - 3 = 0

Move

3

to the right side

3 tan (\frac{x}{2}) - 3 = 0

Add

3

to both sides

3 tan (\frac{x}{2}) - 3 + 3 = 0 + 3

Simplify

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

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

Divide both sides by

3

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

Divide both sides by

3

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

Simplify

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

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

General solutions for

tan (\frac{x}{2}) = \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}

\frac{x}{2} = \frac{π}{6} + πn

\frac{x}{2} = \frac{π}{6} + πn

Solve

\frac{x}{2} = \frac{π}{6} + πn : x = \frac{π}{3} + 2 πn

\frac{x}{2} = \frac{π}{6} + πn

Multiply both sides by

2

\frac{x}{2} = \frac{π}{6} + πn

Multiply both sides by

2

\frac{2 x}{2} = 2 \cdot \frac{π}{6} + 2 πn

Simplify

\frac{2 x}{2} = 2 \cdot \frac{π}{6} + 2 πn

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

2 \cdot \frac{π}{6} + 2 πn : \frac{π}{3} + 2 πn

2 \cdot \frac{π}{6} + 2 πn

2 \cdot \frac{π}{6} = \frac{π}{3}

2 \cdot \frac{π}{6}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{6}

Cancel the common factor:

2

= \frac{π}{3}

= \frac{π}{3} + 2 πn

x = \frac{π}{3} + 2 πn

x = \frac{π}{3} + 2 πn

x = \frac{π}{3} + 2 πn

x = \frac{π}{3} + 2 πn

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

8 cos^{2} (x) + 10 cos (x) + 3 = 0

sin (3 x) = 1, 0 \leq x < 2 π

\frac{2}{π} = sin (x)

1 - 3 cos (x) = 0

What is the general solution for 3tan(x/2)-sqrt(3)=0 ?
The general solution for 3tan(x/2)-sqrt(3)=0 is x= pi/3+2pin