(cos75*cos15-cos15*cos105)/(sin18*sin63+sin108*sin27)

Question

(cos75*cos15-cos15*cos105)/(sin18*sin63+sin108*sin27)

Answer 1

(cos75*cos15-cos15*cos105)/(sin18*sin63+sin108*sin27)=

=(сos(90-15)cos15-cos15cos(90-15))/(sin(90+18)sin27+sin18sin(90-27))=

=(sin15cos15+cos15sin15)/(cos18sin27+sin18cos27)=sin30/sin(45)=(1/2)/(sqrt(2)/2)=

=sqrt(2)/2