What is the value of cos(5/12 pi) ?

The value of cos(5/12 pi) is (sqrt(6)-sqrt(2))/4

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cos(5/12 pi)

cos (\frac{5}{12} π)

\frac{6 - 2}{4}

Solution steps

cos (\frac{5}{12} π)

Simplify:

\frac{5}{12} π = \frac{5 π}{12}

= cos (\frac{5 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 0^{\circ}) \cdot 3

3 cos (\frac{5 π}{6})

cosh (- 2)

sin (- \frac{π}{5})

cot (arcsin (- \frac{2}{8}))

What is the value of cos(5/12 pi) ?
The value of cos(5/12 pi) is (sqrt(6)-sqrt(2))/4