How do you express cos(pi/ 2 ) * cos (( 17 pi) / 12 ) cos(π2)cos(17π12) without using products of trigonometric functions?

1 Answer
Jan 5, 2016

1/2(cos((23pi)/12)+cos((-11pi)/12))12(cos(23π12)+cos(11π12))

Explanation:

Use the rule:

cos(a)cos(b)=1/2(cos(a+b)+cos(a-b))cos(a)cos(b)=12(cos(a+b)+cos(ab))

Thus,

cos(pi/2)cos((17pi)/12)=1/2(cos(pi/2+(17pi)/12)+cos(pi/2-(17pi)/12))cos(π2)cos(17π12)=12(cos(π2+17π12)+cos(π217π12))

=1/2(cos((23pi)/12)+cos((-11pi)/12))=12(cos(23π12)+cos(11π12))

This could continue to be simplified using half angle formulas, but this answer is fine as is given the parameters ("without using products of trigonometric functions").