不用计算器求值 cos^派/8加cos^4 3派/8加cos^4 5派/8加cos^4 7派/8

不用计算器求值 cos^派/8加cos^4 3派/8加cos^4 5派/8加cos^4 7派/8
不用计算器求值 cos^派/8加cos^4 3派/8加cos^4 5派/8加
cos^4 7派/8

不用计算器求值 cos^派/8加cos^4 3派/8加cos^4 5派/8加cos^4 7派/8
cos^4（π/8）+cos^4（ 3π/8）+cos^4（ 5π/8）+cos^4（ 7π/8）
=2[cos(π/8)]^4+2[sin(π/8)]^4
=2-[2sin(π/8)cos(π/8)]^2
=2-[sin(π/4)]^2
=2-1/2
=3/2.