Question 424608
Note that (cos 1)(cos 2)...(cos 45)(csc 46)..(csc 89) = ((cos 1)(cos 2)...(cos 45))/((sin 46)(sin 47)...(sin 89)). Since sin a = cos (90-a), this expression is equal to ((cos 1)(cos 2)...(cos 45))/((cos 44)(cos 43)...(cos 1)). Everything except the cos 45 cancels out, so our expression is equal to cos 45, or {{{sqrt(2)/2}}}.