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

The value of cos((5pi)/4-pi/6) is (sqrt(2)(-sqrt(3)-1))/4

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

cos (\frac{5 π}{4} - \frac{π}{6})

\frac{2 ( - 3 - 1 )}{4}

Solution steps

cos (\frac{5 π}{4} - \frac{π}{6})

Simplify:

\frac{5 π}{4} - \frac{π}{6} = \frac{13 π}{12}

= cos (\frac{13 π}{12})

Rewrite using trig identities:

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

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

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

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

= \frac{2 ( - 3 - 1 )}{4}

cos^{2} (7 5^{\circ}) - sin^{2} (7 5^{\circ})

tan (- \frac{13 π}{6})

4 sin (\frac{3 π}{4})

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

arccos (cos (\frac{9 π}{10}))

What is the value of cos((5pi)/4-pi/6) ?
The value of cos((5pi)/4-pi/6) is (sqrt(2)(-sqrt(3)-1))/4