How do you evaluate $cos 15$ ?

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Answer 1 · 2015-11-06T23:06:46

$cos15=(sqrt(sqrt(3)+2))/2$

To find this value we can use the fact, that we know $cos30$
( $cos30=sqrt(3)/2$ )

$cos30=cos2*15=cos^2 15-sin^2 15$

On the other hand $sin^2 15+cos^2 15=1$ , so we can make a system of equations:

To simplify the notation I will use $s$ for $sin15$ and $c$ for $cos15$

${(c^2+s^2=1),(c^2-s^2=sqrt(3)/2) :}$

If we add both sides of the equations we get:

$2c^2=(2+sqrt(3))/2$

$c^2=(2+sqrt(3))/4$

And finally $c=(sqrt(2+sqrt(3)))/2$

How do you evaluate cos 15cos 15?