How do you find the exact value of $cos15$ using the half-angle identity?

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How do you find the exact value of $cos15$ using the half-angle identity?

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Answer 1 · 2015-02-08T02:29:21

Solution

$cos 30^0 = sqrt(3)/2$
$cos(2*15^0)=sqrt(3)/2$
$2cos^2(15^0)-1=sqrt(3)/2$
$2cos^2(15^0)=(sqrt(3)+2)/2$
$cos^2(15^0)=(sqrt(3)+2)/4$
$cos(15^0)=sqrt((sqrt(3)+2))/2$

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How do you find the exact value of $cos15$ using the half-angle identity?

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How do you find the exact value of $cos15$ using the half-angle identity?