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)#