(sin22градусов * cos8градусов + cos158градусов * cos98градусов) / (sin23градусов *...

пишу без градусов

$\frac{sin22cos8+cos158cos98}{sin23cos7+cos157cos97}=\\ \frac{sin(180-158)cos8+cos158cos(90+8)}{sin(180-157)cos7+cos157cos(90+7)}=\\$

$=\frac{(sin180cos158-cos180sin158)cos8+cos158(cos90cos8-sin90sin8)}{sin180cos157-cos180sin157)cos7+cos157(cos90cos7-sin90sin7)}=$

$=\frac{sin158cos8+cos158(-sin8)}{sin157cos7+cos157(-sin7)}=\\ =\frac{sin158cos8-cos158sin8}{sin157cos7-cos157sin7}=\\ =\frac{sin(158-8)}{sin(157-7)}=\frac{sin150}{sin150}=1$