题目内容：

如何证明Sinx+Cosx=根号2*Cos（x-π/2）
等号右边 根号2乘以Cos[x-(π/2)]，不能证明请写出详细步骤

优质解答

Sin(x)+Cos(x)
=√2[(1/√2)Sin(x)+(1/√2)Cos(x)]
=√2[Sin(π/4)Sin(x)+Cos(π/4)Cos(x)]
=√2Cos(x-π/4)
其中用到公式
Cos(x+y)=Cos(x)Cos(y)-Sin(x)Sin(y)
把y=-π/4,带入即得
Cos(x-π/4)=Cos(x)Cos(π/4)+Sin(x)Sin(π/4)
而Cos(π/4)=Sin(π/4)=1/√2