cosX+sinX=根号2sin(X+π/4)是怎么推出来的,

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cosX+sinX=根号2sin(X+π/4)是怎么推出来的,cosX+sinX=根号2sin(X+π/4)是怎么推出来的,cosX+sinX=根号2sin(X+π/4)是怎么推出来的,sinx+co

cosX+sinX=根号2sin(X+π/4)是怎么推出来的,
cosX+sinX=根号2sin(X+π/4)是怎么推出来的,

cosX+sinX=根号2sin(X+π/4)是怎么推出来的,
sinx+cosx
=√2(√2/2*sinx+√2/2cosx)
=√2(sinxcosπ/4+cosxsinπ/4)
=√2sin(x+π/4)

f(x)=cosx+sinx=√2(√2/2cosx+√2/2sinx)=√2(sin45cosx+cos45sinx)=√2sin(45+x)