What is the value of tan(pi/3)-tan(pi/6) ?

The value of tan(pi/3)-tan(pi/6) is sqrt(3)-(sqrt(3))/3

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tan(pi/3)-tan(pi/6)

tan (\frac{π}{3}) - tan (\frac{π}{6})

3 - \frac{3}{3}

Decimal Notation

1.15470 \dots

Solution steps

tan (\frac{π}{3}) - tan (\frac{π}{6})

Use the following trivial identity:

tan (\frac{π}{3}) = 3

tan (\frac{π}{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}

= 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}

= 3 - \frac{3}{3}

cos (\frac{2 π}{3}) - arctan (1)

cot (arccos (- \frac{2}{5}))

40 sin (7 0^{\circ})

58 sin (6 0^{\circ})

8 cos (5 1^{\circ})

What is the value of tan(pi/3)-tan(pi/6) ?
The value of tan(pi/3)-tan(pi/6) is sqrt(3)-(sqrt(3))/3