What is the value of cos((5pi)/(12))cos(pi/4)+sin((5pi)/(12))sin(pi/4) ?

The value of cos((5pi)/(12))cos(pi/4)+sin((5pi)/(12))sin(pi/4) is (sqrt(3))/2

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cos((5pi)/(12))cos(pi/4)+sin((5pi)/(12))sin(pi/4)

cos (\frac{5 π}{12}) cos (\frac{π}{4}) + sin (\frac{5 π}{12}) sin (\frac{π}{4})

\frac{3}{2}

Solution steps

cos (\frac{5 π}{12}) cos (\frac{π}{4}) + sin (\frac{5 π}{12}) sin (\frac{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}

sec (- \frac{11 π}{6})

arctan (\frac{13}{9})

\frac{1}{sin ( \frac{π}{2} )}

cos (9 1^{\circ})

cos (\frac{π}{8}) + i sin (\frac{π}{8})

What is the value of cos((5pi)/(12))cos(pi/4)+sin((5pi)/(12))sin(pi/4) ?
The value of cos((5pi)/(12))cos(pi/4)+sin((5pi)/(12))sin(pi/4) is (sqrt(3))/2