f（x）=sinx+cosx=根号2*(sinxcos45+cosxsin45)=根号2*sin(x+45怎么转换来的呢

Question

f（x）=sinx+cosx=根号2*(sinxcos45+cosxsin45)=根号2*sin(x+45 怎么转换来的呢

Answer 1

f(x)=sinx+cosx
=√2(sinx*√2/2+cosx*√2/2)---------------提因式√2,为了恒等,各项除以√2.明白?
=√2（sinxcos45°+cosxsin45°)------------该记牢的常识,sin45°=cos45°=√2/2
=√2sin(x+45°)--------------------------知识,sinacosb+cosasinb=sin(a+b)