求证:sin(π/4+x)/sin(π/4-x)+cos(π/4+x)/(π/4-x)=2/cos2x
问题描述：
求证:sin(π/4+x)/sin(π/4-x)+cos(π/4+x)/(π/4-x)=2/cos2x
sin(π/4+x)/sin(π/4-x)+cos(π/4+x)/cos(π/4-x)=2/cos2x
答
证明：
sin(π/4+x)/sin(π/4-x)+cos(π/4+x)/(π/4-x)?
最后少了一个三角函数符号,请核对题目后追问.sin(π/4+x)/sin(π/4-x)+cos(π/4+x)/cos(π/4-x)=2/cos2xsin(π/4+x)/sin(π/4-x)+cos(π/4+x)/cos(π/4-x)=2/cos2x证明： sin(π/4+x)/sin(π/4-x)+cos(π/4+x)/cos(π/4-x)=sin(π/4+x)/cos(π/4+x)+cos(π/4+x)/sin(π/4+x)=[sin²(π/4+x)]/[sin(π/4+x)cos(π/4+x)]+[cos²(π/4+x)/[sin(π/4+x)cos(π/4+x)]=1/[sin(π/4+x)*cos(π/4+x)]=2/[2sin(π/4+x)*cos(π/4+x)] =2/sin(π/2+2x)=2/cos2x