What is the value of 3csc(60)-cot(30) ?

The value of 3csc(60)-cot(30) is square root of 3

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3csc(60)-cot(30)

3 csc (6 0^{\circ}) - cot (3 0^{\circ})

3

Decimal

1.73205 \dots

Solution steps

3 csc (6 0^{\circ}) - cot (3 0^{\circ})

Use the following trivial identity:

csc (6 0^{\circ}) = \frac{2 3}{3}

csc (6 0^{\circ})

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= \frac{2 3}{3}

Use the following trivial identity:

cot (3 0^{\circ}) = 3

cot (3 0^{\circ})

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 3

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

Simplify

3 \cdot \frac{2 3}{3} - 3 : 3

3 \cdot \frac{2 3}{3} - 3

3 \cdot \frac{2 3}{3} = 23

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

Multiply fractions:

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

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

Cancel the common factor:

3

= 23

= 23 - 3

Add similar elements:

23 - 3 = 3

= 3

= 3

94 sin (2 3^{\circ})

\frac{tan ( 3 7 ^{\circ} ) - tan ( 1 3 ^{\circ} )}{1 + ( tan ( 3 7 ^{\circ} ) ) ( tan ( 1 3 ^{\circ} ) )}

\frac{tan ( 22 5 ^{\circ} )}{sin ( 33 0 ^{\circ} )}

4 + 3 cos (\frac{π}{3})

arccos (\frac{1}{2}) + 2 arcsin (\frac{1}{2})

What is the value of 3csc(60)-cot(30) ?
The value of 3csc(60)-cot(30) is square root of 3