分类：教育/科学-理工学科-数学
问题：不查表求值:[1+cos(π/5)][1+cos(3π/5)]. 
回答：∵cos(π/5)+cos(3π/5)=sin(2π/5)/[2sin(π/5)]+[sin(4π/5)-sin(2π/5)]/[2sin(π/5)]=1/2
∴[1+cos(π/5)][1+cos(3π/5)]
=1+cos(π/5)+cos(3π/5)+cos(π/5)cos(3π/5)
=1+1/2+[cos(4π/5)+cos(2π/5)]/2
=3/2+[-cos(π/5)-cos(3π/5)]/2
=5/4