What is the value of 4tan(pi/6)+2cot(pi/3) ?

The value of 4tan(pi/6)+2cot(pi/3) is 2sqrt(3)

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4tan(pi/6)+2cot(pi/3)

4 tan (\frac{π}{6}) + 2 cot (\frac{π}{3})

23

Decimal Notation

3.46410 \dots

Solution steps

4 tan (\frac{π}{6}) + 2 cot (\frac{π}{3})

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

tan (\frac{π}{6})

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{3}{3}

Use the following trivial identity:

cot (\frac{π}{3}) = \frac{3}{3}

cot (\frac{π}{3})

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= \frac{3}{3}

= 4 \cdot \frac{3}{3} + 2 \cdot \frac{3}{3}

Simplify

4 \cdot \frac{3}{3} + 2 \cdot \frac{3}{3} : 23

4 \cdot \frac{3}{3} + 2 \cdot \frac{3}{3}

Add similar elements:

4 \cdot \frac{3}{3} + 2 \cdot \frac{3}{3} = 6 \cdot \frac{3}{3}

= 6 \cdot \frac{3}{3}

Multiply fractions:

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

= \frac{3 \cdot 6}{3}

Divide the numbers:

\frac{6}{3} = 2

= 23

= 23

arccot (- 3.5)

6 sin (1 5^{\circ})

11 cos (6 0^{\circ})

arcsin (\frac{9}{8})

\frac{26}{sin ( 6 4 ^{\circ} )}

What is the value of 4tan(pi/6)+2cot(pi/3) ?
The value of 4tan(pi/6)+2cot(pi/3) is 2sqrt(3)