07 Apr '07 15:06>
Find, without a computer/calculator, the EXACT value of:
Originally posted by sonhouseShouldn't that first one be "not equal to" (\neq) since Cos(x) is less than or equal to one? The equation said something like 2 times ... and so that rang as most likely rong (sic). Suck the wrongness.
Shoudn't that first one be Cos(pi/1)= etc.? otherwise it would just be the Cos(0).
Originally posted by CZekeThe solution is simple...
The answer is actually 1/8, and it's not too hard to get, but the usual trick requires a detour through complex analysis.
Easy part first. We can turn this product of cosines into a sum by using an identity: cos A cos B = 1/2 (cos (A+B) + cos (A-B)). Note that if A-B is negative, we can just turn it positive since cos (-x) = cos x. So...
cos pi/7 cos ...[text shortened]... e first thing any complex analysis student will try -- he's seen too many exercises like this.