函数f(x)=sin(x+ 7派/4)+cos(x- 3派/4)求详细化简过程

问题描述:

函数f(x)=sin(x+ 7派/4)+cos(x- 3派/4)求详细化简过程

f(x)=sin(x-π/4)+cos(x-3π/4)
=sinxcos(π/4)-cosxsin(π/4)+cosxcos(3π/4)+sinxsin(3π/4)
=√2/2(sinx-cosx-cosx+sinx)
=√2(sinx-cosx)
=2(√2/2*sinx-√2/2cosx)
=2sin(x-π/4)