What is the value of tan(30)tan(60) ?

The value of tan(30)tan(60) is 1

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tan(30)tan(60)

tan (3 0^{\circ}) tan (6 0^{\circ})

1

Solution steps

tan (3 0^{\circ}) tan (6 0^{\circ})

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

Use the following trivial identity:

tan (6 0^{\circ}) = 3

tan (6 0^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 3

= \frac{3}{3} 3

Simplify

\frac{3}{3} 3 : 1

\frac{3}{3} 3

Multiply fractions:

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

= \frac{3 3}{3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{3}{3}

Apply rule

\frac{a}{a} = 1

= 1

= 1

sin (\frac{π}{4} + \frac{π}{4})

arccos (\frac{30}{40})

36 \cdot sin (6 0^{\circ})

tan^{2} (\frac{5}{3}) π + 4 sin (\frac{5}{6}) π - 3 cot^{2} (\frac{5}{4}) π

2 + 3 cos (π)