Question

lim x--> 1; log(1-x).cot(πx/2)

Answer 1

limx→1−log(1−x)cosπx2sinπx2=limx→1−1sinπx2⋅limx→1−log(1−x)1cosπx2=l'Hlimx→1−log⁡(1−x)cos⁡πx2sin⁡πx2=limx→1−1sin⁡πx2⋅limx→1−log⁡(1−x)1cos⁡πx2=l'H

=1⋅limx→1−2π−11−x−sinπx2cos2