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

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

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cos((3pi)/4-(5pi)/6)

cos (\frac{3 π}{4} - \frac{5 π}{6})

\frac{6 + 2}{4}

Solution steps

cos (\frac{3 π}{4} - \frac{5 π}{6})

Rewrite using trig identities:

cos (\frac{3 π}{4}) cos (\frac{5 π}{6}) + sin (\frac{3 π}{4}) sin (\frac{5 π}{6})

= cos (\frac{3 π}{4}) cos (\frac{5 π}{6}) + sin (\frac{3 π}{4}) sin (\frac{5 π}{6})

Use the following trivial identity:

cos (\frac{3 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{3 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}

ln (tan (\frac{π}{2}))

sin (\frac{0}{0})

arctan (\frac{13}{3})

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

sin (2 0^{\circ}) cos (10 0^{\circ}) + cos (2 0^{\circ}) sin (10 0^{\circ})

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