摘要
问题试证明:tan 27°=sec 36°-tan 36°.证明:sec 36°-tan 36°=1/cos 36°-sin 36°/cos 36°=1-sin 36°/cos 36°=cos^218°+sin^218°-2 sin 18°·cos 18°/cos^218°-sin^218°=(cos 18°-sin 18°)^2/(cos 18°-sin 18°)(cos 18°+sin 18°)=cos 18°-sin 18°/cos 18°+sin 18°=sin 72°-sin 18°/sin 72°+sin 18°=2 cos 72°+18°/2·sin 72°-18°/2/2 sin 72°+18°/2·cos 72°-18°/2=2 cos 45°·sin 27°/2 sin 45°·cos 27°=tan 27°.
