Question

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

Answer 1

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)

Answer 2

=sin(x-pi/4)+cos(x-3pi/4)
=cos(3pi/4-x)+cos(x-3pi/4)
=2cos(x-3pi/4)

Answer 3

sin(x+7π/4)=sin7π/4cosx+cos7π/4sinx=-√2/2cosx+√2/2sinx
cos(x-3π/4)=cosxcos3π/4+sinxsin3π/4=-√2/2cosx+√2/2sinx
所以，f（x）=（-√2/2cosx+√2/2sinx）*2=2sin（x-π/4）