SOLUTION: Find the exact value of Cos1°*Cos2°*...*Cos45°*Csc46°*...Csc89°

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Question 424608: Find the exact value of Cos1°*Cos2°*...*Cos45°*Csc46°*...Csc89°
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
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%282%29%2F2.