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

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

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

cos (\frac{7 π}{4} - \frac{5 π}{6})

\frac{- 6 - 2}{4}

Solution steps

cos (\frac{7 π}{4} - \frac{5 π}{6})

Simplify:

\frac{7 π}{4} - \frac{5 π}{6} = \frac{11 π}{12}

= cos (\frac{11 π}{12})

Rewrite using trig identities:

cos (\frac{3 π}{4}) cos (\frac{π}{6}) - sin (\frac{3 π}{4}) sin (\frac{π}{6})

= cos (\frac{3 π}{4}) cos (\frac{π}{6}) - sin (\frac{3 π}{4}) sin (\frac{π}{6})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{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}

\frac{4}{cos ( 2 1 ^{\circ} )}

1 + 2 sin (8)

sin (73.7 4^{\circ})

\frac{cot ( π )}{2}

cos (20 7^{\circ})

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