a=sin^2(36°)
b=sin^2(72°)

n=1のとき
(a^(-1)+b^(-1))(a+b)
=(a+b)^2/(ab)
=(sin^2(36°)+sin^2(72°))^2/(sin^2(36°)sin^2(72°))
=(sin^2(36°)+4sin^2(36°)cos^2(36°))^2/(sin^2(36°)4sin^2(36°)cos^2(36°))
=(1+4cos^2(36°))^2/(4cos^2(36°))
=(1+8cos^2(36°)+16cos^4(36°))/(4cos^2(36°))
=(1+8(1-sin^2(36°))+16(1-sin^2(36°))^2)/(4(1-sin^2(36°)))
=(1+8-8sin^2(36°)+16-32sin^2(36°)+16sin^4(36°))/(4(1-sin^2(36°)))
=(25-40sin^2(36°)+16sin^4(36°))/(4(1-sin^2(36°)))
=(25-40sin^2(36°)+20sin^2(36°)-5)/(4(1-sin^2(36°)))
=(20-20sin^2(36°))/(4(1-sin^2(36°)))=5