What is the value of cos((5pi)/4-(7pi)/6) ?

The value of cos((5pi)/4-(7pi)/6) is (sqrt(6)+sqrt(2))/4

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cos((5pi)/4-(7pi)/6)

cos (\frac{5 π}{4} - \frac{7 π}{6})

\frac{6 + 2}{4}

Solution steps

cos (\frac{5 π}{4} - \frac{7 π}{6})

Simplify:

\frac{5 π}{4} - \frac{7 π}{6} = \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}

- cos (2) (\frac{π}{2})

arcsin (\frac{5}{12 sin ( 3 5 ^{\circ} )})

15 cos (0)

15 cos (\frac{π}{3})

\frac{6.9}{sin ( 5 0 ^{\circ} )}

What is the value of cos((5pi)/4-(7pi)/6) ?
The value of cos((5pi)/4-(7pi)/6) is (sqrt(6)+sqrt(2))/4