What is the value of cos(-pi/(12)) ?

The value of cos(-pi/(12)) is (sqrt(6)+sqrt(2))/4

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cos(-pi/(12))

cos (- \frac{π}{12})

\frac{6 + 2}{4}

Solution steps

cos (- \frac{π}{12})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{π}{12}) = cos (\frac{π}{12})

= cos (\frac{π}{12})

Rewrite using trig identities:

cos (\frac{π}{4}) cos (\frac{π}{6}) + sin (\frac{π}{4}) sin (\frac{π}{6})

= cos (\frac{π}{4}) cos (\frac{π}{6}) + sin (\frac{π}{4}) sin (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

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

Simplify

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2} : \frac{6 + 2}{4}

= \frac{6 + 2}{4}

sin (3 x) = 0

sin (\frac{π}{3})

sin (θ) = \frac{2}{2}

arccot (- 3)

arcsin (- \frac{2}{2})

What is the value of cos(-pi/(12)) ?
The value of cos(-pi/(12)) is (sqrt(6)+sqrt(2))/4