What is the value of (cot(60))(sec(45)) ?

The value of (cot(60))(sec(45)) is sqrt(2/3)

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(cot(60))(sec(45))

(cot (6 0^{\circ})) (sec (4 5^{\circ}))

\frac{2}{3}

Decimal Notation

0.81649 \dots

Solution steps

(cot (6 0^{\circ})) (sec (4 5^{\circ}))

= cot (6 0^{\circ}) sec (4 5^{\circ})

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 (4 5^{\circ}) = 2

sec (4 5^{\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}

= 2

= \frac{3}{3} 2

Simplify

\frac{3}{3} 2 : \frac{2}{3}

\frac{3}{3} 2

Multiply fractions:

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

= \frac{3 2}{3}

Apply radical rule:

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

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

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

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

Subtract the numbers:

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

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

Apply radical rule:

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

= \frac{2}{3}

Combine same powers :

\frac{x}{y} = \frac{x}{y}

= \frac{2}{3}

= \frac{2}{3}

sin (4 5^{\circ}) cos (6 0^{\circ}) + cos (4 5^{\circ}) sin (6 0^{\circ})

arctan (\frac{28}{45})

\frac{600}{sin ( 26.5 7 ^{\circ} )}

arccos (\frac{7}{16})

sin (183 0^{\circ})

What is the value of (cot(60))(sec(45)) ?
The value of (cot(60))(sec(45)) is sqrt(2/3)