How do you find the exact value of $cos((2pi)/3)+cos(pi/6)$ ?

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Answer 1 · 2018-02-24T14:09:43

$(sqrt(3)-1)/2$

The angle $theta = (2pi)/3$ is located in the interval $(pi/2,pi)$ so that means $cos(theta)=-cos(pi-theta)$ .

$cos((2pi)/3) = -cos(pi-(2pi)/3) = -cos(pi/3)$

Now, cosine of $pi/3$ ( $60°$ ) is $1/2$ .

So $cos((2pi)/3) = -1/2$

$pi/6 = 30°$ , so
$cos(pi/6) = sqrt3/2$

In conclusion,

$cos((2pi)/3) + cos(pi/6) = -1/2+sqrt3/2 = (sqrt3-1)/2$ .

How do you find the exact value of cos((2pi)/3)+cos(pi/6)cos((2pi)/3)+cos(pi/6)?