How do you simplify $cos (2π/3 - a)$ ?

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Answer 1 · 2016-01-15T03:47:30

$(sqrt3sin(a)-cos(a))/2$

We know the cosine subtraction formula:

$cos(alpha-beta)=cosalphacosbeta+sinalphasinbeta$

Thus,

$cos((2pi)/3-a)=cos((2pi)/3)cos(a)+sin((2pi)/3)sin(a)$

$=-1/2cos(a)+sqrt3/2sin(a)$

This can also be written as

$=(sqrt3sin(a)-cos(a))/2$

How do you simplify cos (2π/3 - a)cos (2π/3 - a)?