What is the value of cos((11pi}{12})cos((3pi)/4)+sin((11pi)/(12))sin(\frac{3pi)/4) ?

The value of cos((11pi}{12})cos((3pi)/4)+sin((11pi)/(12))sin(\frac{3pi)/4) is (sqrt(3))/2

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cos((11pi}{12})cos((3pi)/4)+sin((11pi)/(12))sin(\frac{3pi)/4)

cos (\frac{11 π}{12}) cos (\frac{3 π}{4}) + sin (\frac{11 π}{12}) sin (\frac{3 π}{4})

\frac{3}{2}

Solution steps

cos (\frac{11 π}{12}) cos (\frac{3 π}{4}) + sin (\frac{11 π}{12}) sin (\frac{3 π}{4})

Rewrite using trig identities:

cos (\frac{π}{6})

= cos (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

= \frac{3}{2}

9 sin (\frac{π}{2}) + 9 cos (\frac{π}{2})

50 \cdot cos (4 0^{\circ})

arcsin (0.375)

cos (\frac{4 π}{9}) cos (\frac{π}{9}) + sin (\frac{4 π}{9}) sin (\frac{π}{9})

cot (\frac{5}{4} π)

What is the value of cos((11pi}{12})cos((3pi)/4)+sin((11pi)/(12))sin(\frac{3pi)/4) ?
The value of cos((11pi}{12})cos((3pi)/4)+sin((11pi)/(12))sin(\frac{3pi)/4) is (sqrt(3))/2