What is the value of cos((23pi)/(12)) ?

The value of cos((23pi)/(12)) is (sqrt(2)+sqrt(6))/4

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cos((23pi)/(12))

cos (\frac{23 π}{12})

\frac{2 + 6}{4}

Solution steps

cos (\frac{23 π}{12})

Rewrite using trig identities:

cos (\frac{5 π}{4}) cos (\frac{2 π}{3}) - sin (\frac{5 π}{4}) sin (\frac{2 π}{3})

= cos (\frac{5 π}{4}) cos (\frac{2 π}{3}) - sin (\frac{5 π}{4}) sin (\frac{2 π}{3})

Rewrite using trig identities:

cos (\frac{5 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Rewrite using trig identities:

sin (\frac{5 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

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

Simplify

(- \frac{2}{2}) (- \frac{1}{2}) - (- \frac{2}{2}) \frac{3}{2} : \frac{2 + 6}{4}

= \frac{2 + 6}{4}

sin (20 0^{\circ})

sec (\frac{9 π}{4})

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

\frac{2 tan ( 1 5 ^{\circ} )}{1 - tan ^{2} ( 1 5 ^{\circ} )}

cos (1 π)

What is the value of cos((23pi)/(12)) ?
The value of cos((23pi)/(12)) is (sqrt(2)+sqrt(6))/4