How do you express $cos( (15 pi)/ 8 ) * cos (( 5 pi) /12 )$ without using products of trigonometric functions?

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Answer 1 · 2017-01-23T17:24:24

The answer is $=1/2(cos(55/24pi)+cos(35/24pi))$

$cos(A+B)=cosAcosB-sinAsinB$

$cos(A-B)=cosAcosB+sinAsinB$

$cos(A+B)+cos(A-B)=2cosAcosB$

Therefore,

$cosAcosB=1/2(cos(A+B)+cos(A-B))$

Here,

$A=15/8pi$ and $B=5/12pi$

So,

$cos(15/8pi)cos(5/12pi)=1/2(cos(15/8pi+5/12pi))+cos(15/8pi-5/12pi))$

$=1/2(cos(55/24pi)+cos(35/24pi))$

How do you express cos( (15 pi)/ 8 ) * cos (( 5 pi) /12 ) cos( (15 pi)/ 8 ) * cos (( 5 pi) /12 ) without using products of trigonometric functions?