超难三角函数：(cos36°)^2+(cos72°)^2

cos²36°+ cos²72°
=1/2(1+cos72°)+1/2(1+cos144°)
=1+1/2(cos72°+cos144°)
=1+cos108°cos36°
=1-cos72°cos36°
而 cos36°cos72°
=2sin36°cos36°cos72°/2sin36°
=sin72°cos72°/2sin36°
=1/2sin144°/2sin36°
=1/4
所以cos²36°+ cos²72°=1-1/4=3/4