What is the value of 3tan(60)cot(30)sin(45)csc(45) ?

The value of 3tan(60)cot(30)sin(45)csc(45) is 9

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3tan(60)cot(30)sin(45)csc(45)

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

9

Solution steps

3 tan (6 0^{\circ}) cot (3 0^{\circ}) sin (4 5^{\circ}) csc (4 5^{\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:

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

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

Use the following trivial identity:

csc (4 5^{\circ}) = 2

csc (4 5^{\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

= 333 \frac{2}{2} 2

Simplify

333 \frac{2}{2} 2 : 9

333 \frac{2}{2} 2

Apply radical rule:

a a = a

33 = 3

= 3 \cdot 32 \frac{2}{2}

Multiply fractions:

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

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

2 \cdot 3 \cdot 32 = 18

2 \cdot 3 \cdot 32

Multiply the numbers:

3 \cdot 3 = 9

= 922

Apply radical rule:

a a = a

22 = 2

= 9 \cdot 2

Multiply the numbers:

9 \cdot 2 = 18

= 18

= \frac{18}{2}

Divide the numbers:

\frac{18}{2} = 9

= 9

= 9

\frac{sin ( 3 7 ^{\circ} ) + 3}{2 sin ( 3 7 ^{\circ} )}

cos (2.1)

cos (2.3)

ln (tan (0))

arccsc (7.1)

What is the value of 3tan(60)cot(30)sin(45)csc(45) ?
The value of 3tan(60)cot(30)sin(45)csc(45) is 9