sinx加cosx提出一个根号2怎么等于根号2乘sin（x+π/4）？请写一下详细过程！！！谢谢！！

更新时间2018-11-04 10:35:48

sinx+cosx

=1*sinx+1*cosx

=√2*(1/√2)*sinx+√2*(1/√2)*cosx

=√2*(√2/2)*sinx+√2*(√2/2)*cosx

=√2*[(√2/2)*sinx+(√2/2)*cosx]

=√2*(cos(π/4)*sinx+sin(π/4)*cosx)

=√2*sin(x+π/4)

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