What is the value of 4cos^2(60)+sqrt(3)tan(30) ?

The value of 4cos^2(60)+sqrt(3)tan(30) is 2

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4cos^2(60)+sqrt(3)tan(30)

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

2

Solution steps

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

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}

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}

= 4 (\frac{1}{2})^{2} + 3 \frac{3}{3}

Simplify

4 (\frac{1}{2})^{2} + 3 \frac{3}{3} : 2

4 (\frac{1}{2})^{2} + 3 \frac{3}{3}

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

4 (\frac{1}{2})^{2}

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

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

Apply exponent rule:

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

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

Apply rule

1^{a} = 1

1^{2} = 1

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

= 4 \cdot \frac{1}{2 ^{2}}

Multiply fractions:

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

= \frac{1 \cdot 4}{2 ^{2}}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4}{2 ^{2}}

Factor

4 : 2^{2}

Factor

4 = 2^{2}

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

Cancel the common factor:

2^{2}

= 1

3 \frac{3}{3} = 1

3 \frac{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 + 1

Add the numbers:

1 + 1 = 2

= 2

= 2

cos (π - \frac{π}{3})

\frac{12.2}{sin ( 4 0 ^{\circ} )}

cos (3 0^{\circ}) sin (4 5^{\circ}) + sin (3 0^{\circ}) tan (3 0^{\circ})

sin (252 0^{\circ})

tan (arcsin (\frac{- 4}{5}))

What is the value of 4cos^2(60)+sqrt(3)tan(30) ?
The value of 4cos^2(60)+sqrt(3)tan(30) is 2