What is the value of 6tan^2(30)+20cos(60) ?

The value of 6tan^2(30)+20cos(60) is 12

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6tan^2(30)+20cos(60)

6 tan^{2} (3 0^{\circ}) + 20 cos (6 0^{\circ})

12

Solution steps

6 tan^{2} (3 0^{\circ}) + 20 cos (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:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 0^{\circ})

cos (x)

periodicity table with

36 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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

= 6 (\frac{3}{3})^{2} + 20 \cdot \frac{1}{2}

Simplify

6 (\frac{3}{3})^{2} + 20 \cdot \frac{1}{2} : 12

6 (\frac{3}{3})^{2} + 20 \cdot \frac{1}{2}

6 (\frac{3}{3})^{2} = 2

6 (\frac{3}{3})^{2}

(\frac{3}{3})^{2} = \frac{1}{3}

(\frac{3}{3})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 3 ) ^{2}}{3 ^{2}}

(3)^{2} : 3

Apply radical rule:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

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

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 3

= \frac{3}{3 ^{2}}

Cancel the common factor:

3

= \frac{1}{3}

= 6 \cdot \frac{1}{3}

Multiply fractions:

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

= \frac{1 \cdot 6}{3}

Multiply the numbers:

1 \cdot 6 = 6

= \frac{6}{3}

Divide the numbers:

\frac{6}{3} = 2

= 2

20 \cdot \frac{1}{2} = 10

20 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 20}{2}

Multiply the numbers:

1 \cdot 20 = 20

= \frac{20}{2}

Divide the numbers:

\frac{20}{2} = 10

= 10

= 2 + 10

Add the numbers:

2 + 10 = 12

= 12

= 12

100 cos (15 0^{\circ})

tan (63.4 3^{\circ})

\frac{1}{sin ( 2 5 ^{\circ} )}

5.7 tan (2 6^{\circ})

arctan (\frac{4}{7}) + arctan (\frac{7}{4})

What is the value of 6tan^2(30)+20cos(60) ?
The value of 6tan^2(30)+20cos(60) is 12