如何得到f(x)=|sinx+cosx|=|根号2sin(x+π/4)|?请写出详细的步骤

如何得到f(x)=|sinx+cosx|=|根号2sin(x+π/4)|?请写出详细的步骤
如何得到f(x)=|sinx+cosx|=|根号2sin(x+π/4)|?
请写出详细的步骤

如何得到f(x)=|sinx+cosx|=|根号2sin(x+π/4)|?请写出详细的步骤
f(x)=|sinx+cosx|
=|√2（√2/2*sinx+√2/2*cosx|
=|√2（sinx*cosπ/4+cosx*sinπ/4）|
=|√2sin(x+π/4)|.

f(x)=|sinx+cosx|=
=√2|√2/2*sinx+√2/2*cosx|
=√2|sinxcosπ/4+cosxsinπ/4|
=√2|sin(x+π/4)|

sin(x+π/4)=sinxcosπ/4+cosxsinπ/4=√2/2 *(sinx+cosx)
|√2sin(x+π/4)|=|)|√2*√2/2 (sinx+cosx)|=|sinx+cosx|