Question

证明tan72=tan18+tan^254

Answer 1

问：证明tan72=tan18+tan^254

答：假设一个顶角36度,底角72度的等腰三角形ABC,〈A=36度,〈B=〈C=72度，则sin18°=CE/AC=（1/2）/[(√5+1）/2]=（√5-1）/4,cos72°=sin18°=（√5-1）/4,AE=√（AC^2-CE^2)=√(5+2√5)/2,sin72°=AE/AC=)=√(10+2√5)/4,故tan72°=AE/CE=√(5+2√5)=3.077683…所以得tan(72°)等于3.077683……