What is the value of cos(pi/4-(5pi)/6) ?

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

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cos(pi/4-(5pi)/6)

cos (\frac{π}{4} - \frac{5 π}{6})

\frac{- 6 + 2}{4}

Solution steps

cos (\frac{π}{4} - \frac{5 π}{6})

Rewrite using trig identities:

cos (\frac{π}{4}) cos (\frac{5 π}{6}) + sin (\frac{π}{4}) sin (\frac{5 π}{6})

= cos (\frac{π}{4}) cos (\frac{5 π}{6}) + sin (\frac{π}{4}) sin (\frac{5 π}{6})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

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

Simplify

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

= \frac{- 6 + 2}{4}

9 sin (\frac{π}{4}) + 9 cos (\frac{π}{4})

arccos (\frac{3}{14})

cos (2 (\frac{π}{4}))

arctan (\frac{5}{- 3})

sin (\frac{π}{2}) + cos (\frac{π}{2})

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