How do you evaluate $cos(pi/3 - pi/6)$ ?

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Answer 1 · 2016-06-03T15:15:36

If we momentarily forgot how to subtract fractions, we could use the cosine subtraction formula:

$cos(A-B)=cos(A)cos(B)+sin(A)sin(B)$

So, we see that

$cos(pi/3-pi/6)=cos(pi/3)cos(pi/6)+sin(pi/3)sin(pi/6)$

$=1/2(sqrt3/2)+sqrt3/2(1/2)$

$=sqrt3/4+sqrt3/4$

$=(2sqrt3)/4$

$=sqrt3/2$

How do you evaluate cos(pi/3 - pi/6)cos(pi/3 - pi/6)?