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})

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^{2} (x) - 1 = 0

cot (6 0^{\circ})

sec^{2} (\frac{π}{2})

cos (3 θ) = - 1

sin (θ) + 1 = 0

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