sinx+cosx可以用和差化积公式算吗? 三角函数积化和差,和差化积公式
\u222b1/(sinx+cosx)dx\u4e2d\u5408\u5e76sinx+cosx\u4e2d\u4e3a\u4ec0\u4e48\u4e0d\u80fd\u7528\u548c\u5dee\u5316\u79ef\u516c\u5f0f\uff1f\u4f60\u7684\u548c\u5dee\u5316\u79ef\u516c\u5f0f\u8bb0\u9519\u4e86\u628asinA+sinB=2sin(A+B)/2 *cos(A-B)/2sinA+cosB\u662f\u6ca1\u6709\u516c\u5f0f\u7684
\u548c\u5dee\u5316\u79ef
sinx+siny=2sin[(x+y)/2]cos[(x-y)/2]
sinx-siny=2cos[(x+y)/2]sin[(x-y)/2]
cosx+cosy=2cos[(x+y)/2]cos[(x-y)/2]
cosx-cosy=-2sin[(x+y)/2]sin[(x-y)/2]
\u79ef\u5316\u548c\u5dee
sinxsiny=-1/2[cos(x+y)-cos(x-y)]
cosxcosy=1/2[cos(x+y)+cos(x-y)]
sinxcosy=1/2[sin(x+y)+sin(x-y)]
cosxsiny=1/2[sin(x+y)-sin(x-y)]
你写的这个:sinx+cosx是不同的三角函数,要想用和差化积,先要进行恒等变形:
sinx+cosx=cos(π/2 -x)+cosx)
或
sinx+cosx=sinx+sin(π/2 -x)
然后再运用和差化积公式进行计算。
最后还要化简。
因为是自找麻烦,所以过程不写了,太复杂。
本题化简很简单:
sinx+cosx=√2sin(x+π/4)
你的和差化积公式记错了把
sina+sinb=2sin(a+b)/2
*cos(a-b)/2
sina+cosb是没有公式的
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