dokazati togdestvo cos36-cos72=1/2

Question

dokazati togdestvo cos36-cos72=1/2

Answer 1

cos36=cos(90-54)=sin54

cos72=cos(90-18)=sin18

 

cos36 -cos72=

=2sin(18)sin(54)=0.5sin(2*18)sin(2*54)/(cos(18)cos(54))=0.5sin(36)sin(108)/(sin(108)sin(36))=0.5.

Следовательно cos36-cos72=1/2.