灵鹊做题网三角函数,能写在纸上最好
来源：学生作业帮 编辑：灵鹊做题网作业帮 分类：数学作业 时间：2024/06/16 08:44:49
三角函数,能写在纸上最好
sin^4(Π/16)+sin^4( 3Π /16)+sin^4( 5Π/16)+sin^4(7Π/16)
=sin^4(Π/16)+sin^4(7Π/16)+sin^4( 3Π /16)+sin^4( 5Π/16)
=sin^4(Π/16)+cos^4(Π/16)+sin^4( 3Π /16)+cos^4( 3Π/16)
=1-2sin^2(Π/16)cos^2(Π/16)+1-2sin^2(3Π/16)cos^2(3Π/16)
=2-(sinΠ/4)^2/2-(sin3Π/4)^2/2
=2-1/2
=3/2
=sin^4(Π/16)+sin^4(7Π/16)+sin^4( 3Π /16)+sin^4( 5Π/16)
=sin^4(Π/16)+cos^4(Π/16)+sin^4( 3Π /16)+cos^4( 3Π/16)
=1-2sin^2(Π/16)cos^2(Π/16)+1-2sin^2(3Π/16)cos^2(3Π/16)
=2-(sinΠ/4)^2/2-(sin3Π/4)^2/2
=2-1/2
=3/2