Докажите равенство: cos75*cos 15=1/4

Question

Докажите равенство: cos75*cos 15=1/4

Answer 1

Cos(90-15)cos15= sin15cos15= ¹/₂ * 2sin15cos15= ¹/₂ sin(2*15)=
=¹/₂ sin30=¹/₂ * ¹/₂= 1/4

Answer 2

Cos75°cos15°=1/4,cos75°=cos(90°-15°)=
=sin15°cos75°cos15°= sin15°cos15°=
=0,5·(2 sin15°cos15°)=0,5·sin30°=0,5·0,5=0.25=1/4