Покажите истинность равенства cos 64 cos4-cos86 cos26/cos71 cos 3+cos87 cos19

Question

Покажите истинность равенства cos 64 cos4-cos86 cos26/cos71 cos 3+cos87 cos19

Answer 1

(cos64°cos4°- cos86°cos26°)/(cos71°cos41°-cos49°cos19° ) =
(cos (90°-26°)cos4°-cos((90°-4°)cos26°)/(cos(90°-19°)cos41°-cos(90°-41°)cos19°))=
(sin26°cos4°-sin4°cos26°)/(sin19°cos41°-sin41°cos19°))=sin22°/sin(-22°)=-1