What is the value of csc(30)*tan(45)-cot(60)*sec(30) ?

The value of csc(30)*tan(45)-cot(60)*sec(30) is 4/3

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csc(30)tan(45)-cot(60)sec(30)

Solution

csc (3 0^{\circ}) \cdot tan (4 5^{\circ}) - cot (6 0^{\circ}) \cdot sec (3 0^{\circ})

Solution

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

csc (3 0^{\circ}) tan (4 5^{\circ}) - cot (6 0^{\circ}) sec (3 0^{\circ})

Use the following trivial identity:

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

csc (3 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

= 2

Use the following trivial identity:

tan (4 5^{\circ}) = 1

tan (4 5^{\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}

= 1

Use the following trivial identity:

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

cot (6 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

= \frac{3}{3}

Use the following trivial identity:

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

sec (3 0^{\circ})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= \frac{2 3}{3}

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

Simplify

2 \cdot 1 - \frac{3}{3} \cdot \frac{2 3}{3} : \frac{4}{3}

2 \cdot 1 - \frac{3}{3} \cdot \frac{2 3}{3}

2 \cdot 1 = 2

2 \cdot 1

Multiply the numbers:

2 \cdot 1 = 2

= 2

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

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

Multiply fractions:

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

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

Multiply the numbers:

3 \cdot 3 = 9

= \frac{6}{9}

Cancel the common factor:

3

= \frac{2}{3}

= 2 - \frac{2}{3}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

2 \cdot 3 - 2 = 4

2 \cdot 3 - 2

Multiply the numbers:

2 \cdot 3 = 6

= 6 - 2

Subtract the numbers:

6 - 2 = 4

= 4

= \frac{4}{3}

= \frac{4}{3}

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7 cos (5 3^{\circ})

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40 sin (12 0^{\circ})

e^0*cos(0)

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cos^{2} (π) - 3 sin (π)

arctan((1.33)/1)

arctan (\frac{1.33}{1})

Frequently Asked Questions (FAQ)

What is the value of csc(30)*tan(45)-cot(60)*sec(30) ?
The value of csc(30)*tan(45)-cot(60)*sec(30) is 4/3