Question

三角比计算

（ 1+cos π/5 )( 1+cos 3π/5 ）＝？

（完整过程）

Answer 1

[1+cos(π/5)][1+cos(3π/5)]
=1+cos(π/5)+cos(3π/5)+cos(π/5)cos(3π/5)
=1+2cos(2π/5)·cos(π/5)-cos(π/5)cos(2π/5)【因为cos(3π/5)=-cos(2π/5)】
=1+cos(π/5)cos(2π/5)
=1+[2sin(π/5)cos(π/5)cos(2π/5)]/[2sin(π/5)]
=1+[sin(2π/5)cos(2π/5)]/[2sin(π/5)]
=1+[2sin(2π/5)cos(2π/5)]/[4sin(π/5)]
=1+[sin(4π/5)]/[4sin(π/5)]
=1+(1/4)
=5/4