为什么sin(x+π/4)的平方等于cos(x-π/4)的平方?
问题描述:
为什么sin(x+π/4)的平方等于cos(x-π/4)的平方?
答
{sin(x+π/4)}^2
={sin[(x-π/4)+π/2]}^2
={sin(x-π/4)cos(π/2)+cos(x-π/4)sin(π/2)}^2
={sin(x-π/4)·0+cos(x-π/4)·1}^2
={cos(x-π/4}^2
答
sin(x+π/4)=sinxcosπ/4+cosxsinπ/4=√2/2(sinx+cosx)
cos(x-π/4)=cosxcosπ/4+sinxsinπ/4=√2/2(sinx+cosx)
这种根据正余弦公式比较容易理解
答
法一:sin(x+π/4)=sinxcosπ/4+cosxsinπ/4=√2/2(sinx+cosx)cos(x-π/4)=cosxcosπ/4+sinxsinπ/4=√2/2(sinx+cosx)所以相等.法二:sin(x+π/4)=sin(x+π/2-π/4)=sin[π/2-(π/4-x)]=cos(π/4-x)=cos(x-π/4...