Question #8b831

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Answer 1 · 2017-02-12T15:19:24

$cos15=cos(45-30)$

expanding by using

$cos(x-y)=cosxcosy+sinxsiny$

$cos(45-30)=cos45cos30+sin45sin30$

use the standard angle values for cosine and sine

$cos(45-30)=sqrt2/2.sqrt3/2+sqrt2/2. 1/2$

factorise

$cos(45-30)=1/4sqrt2(sqrt3+1)$

multiply $sqrt2$ into the bracket to arrive at required solution

$cos(45-30)=1/4(sqrt6+sqrt2)$