What is the value of 2tan(60)tan(30) ?

The value of 2tan(60)tan(30) is 2

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2tan(60)tan(30)

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

2

Solution steps

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

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

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}

= 23 \frac{3}{3}

Simplify

23 \frac{3}{3} : 2

23 \frac{3}{3}

Multiply fractions:

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

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

3 \cdot 23 = 6

3 \cdot 23

Apply radical rule:

a a = a

33 = 3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

= \frac{6}{3}

Divide the numbers:

\frac{6}{3} = 2

= 2

= 2

5 cos (3 π)

cos (0) - (0) sin (0)

1.5 \cdot tan (3 0^{\circ})

tan (12 7^{\circ})

e^{t a n (0)} sec^{2} (0)