将f(x)=cos2x/cos(π/4+x)化成标准三角函数

将f(x)=cos2x/cos(π/4+x)化成标准三角函数
将f(x)=cos2x/cos(π/4+x)化成标准三角函数

将f(x)=cos2x/cos(π/4+x)化成标准三角函数
f(x)=cos2x/cos(π/4+x)
=(cos²x-sin²x)/(√2/2cosx-√2/2sinx)
=(cosx+sinx)(cosx-sinx)/[√2/2(cosx-sinx)]
=√2(cosx+sinx)
=2(√2/2cosx+√2/2sinx)
=2sin(x+π/4)