sin(a+b)cos(a-b)=sina*cosa+sinb*cosb

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sin(a+b)cos(a-b)=sina*cosa+sinb*cosb
sin(a+b)cos(a-b)=sina*cosa+sinb*cosb

sin(a+b)cos(a-b)=sina*cosa+sinb*cosb
先学基础知识:
积化和差公式:sin(A)*cos(B) = (1/2)*[sin(A+B) + sin(A-B)]
二倍角公式 :sin(2A) = 2*sinAcosA
再做题:
sin(a+b)cos(a-b)
= (1/2)*{sin[(a+b)+(a-b)] + sin[(a+b)-(a-b)]}
= (1/2)*[sin(2a) + sin(2b)]
= (1/2)*[2*sin(a)*cos(a) + 2*sin(b)*cos(b)]
= sin(a)*cos(a) + sin(b)*cos(b)

是要证明吗?
sina*cosa+sinb*cosb
=1/2 * (sin2a+sin2b)
=1/2 * (sin[(a+b)+(a-b)]+sin[(a+b)-(a-b)]
下面按书上的公式做就行了