What is the value of cos(165)cos(15) ?

The value of cos(165)cos(15) is (-sqrt(3)-2)/4

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cos(165)cos(15)

cos (16 5^{\circ}) cos (1 5^{\circ})

\frac{- 3 - 2}{4}

Decimal Notation

- 0.93301 \dots

Solution steps

cos (16 5^{\circ}) cos (1 5^{\circ})

Rewrite using trig identities:

\frac{cos ( 15 0 ^{\circ} ) + cos ( 18 0 ^{\circ} )}{2}

cos (16 5^{\circ}) cos (1 5^{\circ})

Use the Product to Sum identity:

cos (s) cos (t) = \frac{1}{2} (cos (s - t) + cos (s + t))

= \frac{1}{2} (cos (16 5^{\circ} - 1 5^{\circ}) + cos (16 5^{\circ} + 1 5^{\circ}))

Simplify

= \frac{cos ( 15 0 ^{\circ} ) + cos ( 18 0 ^{\circ} )}{2}

= \frac{cos ( 15 0 ^{\circ} ) + cos ( 18 0 ^{\circ} )}{2}

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:

cos (18 0^{\circ}) = (- 1)

cos (18 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}

= (- 1)

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

Simplify

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

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

Join

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

- \frac{3}{2} - 1

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

Multiply the numbers:

1 \cdot 2 = 2

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

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

Apply the fraction rule:

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

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{- 3 - 2}{4}

= \frac{- 3 - 2}{4}

1 + cos (\frac{π}{12})

arcsin (1.8)

arctan (\frac{8.7}{10})

8 cos (2 (0))

cot (\frac{- π}{12})

What is the value of cos(165)cos(15) ?
The value of cos(165)cos(15) is (-sqrt(3)-2)/4