[Serkan A.]

Cos1.Cos3.Cos5....Cos87.Cos89=?

a) 2⁵⁰-1 b) 2^-50+1 c) 2^-50-1 d)2^-99 e) 2^-89/2

Bu gecenin son sorusu olsun.

[gereksizyorumcu]

bize verilen çarpım
=cos1.cos3.cos5....cos45.cos47....cos87.cos89=S olsun
Ç=cos2.cos4....cos44.cos46....cos86.cos88 olsun

S.Ç/cos45=cos1.cos2....cos44.cos46....cos88.cos89
S.Ç.√2=(cos1.cos89).(cos2.cos88)....(cos44.cos46)
S.Ç.√2=[(cos88+cos90)/2].[(cos86+cos90)/2]...[(cos2+cos90)/2]
S.Ç.√2=(cos2.cos4.cos6....cos88)/2⁴⁴ (sanırım farklılık burada)
S.Ç.√2=Ç/2⁴⁴
S=2^-44/√2=2^-44-1/2=2^-89/2