Question 1063574
<pre>
cos(5pi/7)cos(23pi/42) + sin(5pi/7)sin(23pi/42)

Use the identity

{{{cos(alpha-beta)}}}{{{""=""}}}{{{cos(alpha)cos(beta) + sin(alpha)sin(beta)}}}

where {{{alpha=(5pi)/7}}} and {{{beta=23pi/42}}}

{{{cos((5pi)/7-(23pi)/42))}}}{{{""=""}}}{{{cos((5pi)/7)cos((23pi)/42) + sin((5pi)/7)sin((23pi)/42)}}}

{{{cos((6(5pi))/(6*7)-(23pi)/42)}}}{{{""=""}}}{{{cos((5pi)/7)cos((23pi)/42) + sin((5pi)/7)sin((23pi)/42)}}}

{{{cos((30pi)/42-(23pi)/42)}}}{{{""=""}}}{{{cos((5pi)/7)cos((23pi)/42) + sin((5pi)/7)sin((23pi)/42)}}}

{{{cos((7pi)/42)}}}{{{""=""}}}{{{cos((5pi)/7)cos((23pi)/42) + sin((5pi)/7)sin((23pi)/42)}}}

{{{cos(pi/6)}}}{{{""=""}}}{{{cos((5pi)/7)cos((23pi)/42) + sin((5pi)/7)sin((23pi)/42)}}}

{{{sqrt(3)/2}}}

Edwin</pre>