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

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

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

cos (\frac{3 π}{4} - \frac{π}{6})

\frac{- 6 + 2}{4}

Solution steps

cos (\frac{3 π}{4} - \frac{π}{6})

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}

cos (π - \frac{π}{4})

- csc (\frac{π}{3})

cos (- \frac{3}{4})

tan (2 arccos (\frac{12}{13}))

arctan (- \frac{7}{2})

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