What is the value of cos((17pi)/6)*sec(-60)+cot(210) ?

The value of cos((17pi)/6)*sec(-60)+cot(210) is 0

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cos((17pi)/6)*sec(-60)+cot(210)

cos (\frac{17 π}{6}) \cdot sec (- 6 0^{\circ}) + cot (21 0^{\circ})

0

Solution steps

cos (51 0^{\circ}) sec (- 6 0^{\circ}) + cot (21 0^{\circ})

Use the following property:

sec (- x) = sec (x)

sec (- 6 0^{\circ}) = sec (6 0^{\circ})

= cos (51 0^{\circ}) sec (6 0^{\circ}) + cot (21 0^{\circ})

cos (51 0^{\circ}) = cos (15 0^{\circ})

cos (51 0^{\circ})

Rewrite

51 0^{\circ}

36 0^{\circ} + 15 0^{\circ}

= cos (36 0^{\circ} + 15 0^{\circ})

Apply the periodicity of

cos

cos (x + 36 0^{\circ}) = cos (x)

cos (36 0^{\circ} + 15 0^{\circ}) = cos (15 0^{\circ})

= cos (15 0^{\circ})

= cos (15 0^{\circ}) sec (6 0^{\circ}) + cot (21 0^{\circ})

cot (21 0^{\circ}) = cot (3 0^{\circ})

cot (21 0^{\circ})

Rewrite

21 0^{\circ}

18 0^{\circ} + 3 0^{\circ}

= cot (18 0^{\circ} + 3 0^{\circ})

Apply the periodicity of

cot

cot (x + 18 0^{\circ}) = cot (x)

cot (18 0^{\circ} + 3 0^{\circ}) = cot (3 0^{\circ})

= cot (3 0^{\circ})

= cos (15 0^{\circ}) sec (6 0^{\circ}) + cot (3 0^{\circ})

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

cos (15 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{3}{2}

Use the following trivial identity:

sec (6 0^{\circ}) = 2

sec (6 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}

= 2

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

= (- \frac{3}{2}) \cdot 2 + 3

Simplify

(- \frac{3}{2}) \cdot 2 + 3 : 0

(- \frac{3}{2}) \cdot 2 + 3

Remove parentheses:

(- a) = - a

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

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

\frac{3}{2} \cdot 2

Multiply fractions:

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

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

Cancel the common factor:

2

= 3

= - 3 + 3

Add similar elements:

- 3 + 3 = 0

= 0

= 0

sec (\frac{19 π}{3})

- cos (\frac{π}{2} + \frac{π}{2})

sin (arccos (\frac{2}{9}))

\frac{3.7}{tan ( 4.6 )}

ln (2 + tan (\frac{π}{16}))

What is the value of cos((17pi)/6)*sec(-60)+cot(210) ?
The value of cos((17pi)/6)*sec(-60)+cot(210) is 0