What is the general solution for tan(2x-pi/6)= 1/(3^{1/2)} ?

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

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Popular Trigonometry >

tan(2x-pi/6)= 1/(3^{1/2)}

Solution

tan (2 x - \frac{π}{6}) = \frac{1}{3 ^{\frac{1}{2}}}

Solution

x = \frac{π}{6} + \frac{πn}{2}

Degrees

x = 3 0^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 x - \frac{π}{6}) = \frac{1}{3 ^{\frac{1}{2}}}

Apply trig inverse properties

tan (2 x - \frac{π}{6}) = \frac{1}{3 ^{\frac{1}{2}}}

General solutions for

tan (2 x - \frac{π}{6}) = \frac{1}{3 ^{\frac{1}{2}}}

tan (x) = a \Rightarrow x = arctan (a) + πn

2 x - \frac{π}{6} = arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn

2 x - \frac{π}{6} = arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn

Solve

2 x - \frac{π}{6} = arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn : x = \frac{π}{6} + \frac{πn}{2}

2 x - \frac{π}{6} = arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn

Simplify

arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn : \frac{π}{6} + πn

arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn

Use the following trivial identity:

arctan (\frac{1}{3 ^{\frac{1}{2}}}) = \frac{π}{6}

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{6} + πn

2 x - \frac{π}{6} = \frac{π}{6} + πn

Move

\frac{π}{6}

to the right side

2 x - \frac{π}{6} = \frac{π}{6} + πn

Add

\frac{π}{6}

to both sides

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

Simplify

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

Simplify

2 x - \frac{π}{6} + \frac{π}{6} : 2 x

2 x - \frac{π}{6} + \frac{π}{6}

Add similar elements:

- \frac{π}{6} + \frac{π}{6} = 0

= 2 x

Simplify

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

\frac{π}{6} + πn + \frac{π}{6}

Group like terms

= \frac{π}{6} + \frac{π}{6} + πn

Combine the fractions

\frac{π}{6} + \frac{π}{6} : \frac{π}{3}

Apply rule

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

= \frac{π + π}{6}

Add similar elements:

π + π = 2 π

= \frac{2 π}{6}

Cancel the common factor:

2

= \frac{π}{3}

= \frac{π}{3} + πn

2 x = \frac{π}{3} + πn

2 x = \frac{π}{3} + πn

2 x = \frac{π}{3} + πn

Divide both sides by

2

2 x = \frac{π}{3} + πn

Divide both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

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

\frac{\frac{π}{3}}{2} + \frac{πn}{2}

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

Apply the fraction rule:

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

= \frac{π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{π}{6}

= \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

Graph

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Frequently Asked Questions (FAQ)

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