求高中数学中对数的常用变换公式，以及三角函数的和差化积公式 三角函数积化和差公式是什么？
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\u79ef\u5316\u548c\u5dee\u516c\u5f0f\u662f\uff1a
sin\u03b1cos\u03b2=\u3010sin(\u03b1+\u03b2)+sin(\u03b1-\u03b2)\u3011/2
cos\u03b1sin\u03b2 =\u3010sin(\u03b1+\u03b2)-sin(\u03b1-\u03b2)\u3011/2
sin\u03b1sin\u03b2=\u3010cos(\u03b1-\u03b2)-cos(\u03b1+\u03b2)\u3011/2
cos\u03b1cos\u03b2=\u3010cos(\u03b1+\u03b2)+cos(\u03b1-\u03b2)\u3011/2
\u548c\u5dee\u5316\u79ef\u4ee5\u53ca\u79ef\u5316\u548c\u5dee\u516c\u5f0f\u7684\u63a8\u5bfc\u975e\u5e38\u7b80\u5355\u3002
sin(\u03b1+\u03b2)\u3001sin(\u03b1-\u03b2)\u3001cos(\u03b1+\u03b2)\u3001cos(\u03b1-\u03b2)
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\u6269\u5c55\u8d44\u6599\uff1a
\u548c\u5dee\u5316\u79ef\u516c\u5f0f
sin\u03b1\uff0bsin\u03b2\uff1d2sin\uff08\u03b1\uff0b\u03b2\uff09/2\u00b7cos\uff08\u03b1\uff0d\u03b2\uff09/2
sin\u03b1\uff0dsin\u03b2\uff1d2cos\uff08\u03b1\uff0b\u03b2\uff09/2\u00b7sin\uff08\u03b1\uff0d\u03b2\uff09/2
cos\u03b1\uff0bcos\u03b2\uff1d2cos\uff08\u03b1\uff0b\u03b2\uff09/2\u00b7cos\uff08\u03b1\uff0d\u03b2\uff09/2
cos\u03b1\uff0dcos\u03b2\uff1d\uff0d2sin\uff08\u03b1\uff0b\u03b2\uff09/2\u00b7sin\uff08\u03b1\uff0d\u03b2\uff09/2
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a
\u767e\u5ea6\u767e\u79d1-\u79ef\u5316\u548c\u5dee
用^表示乘方，用log(a)(b)表示以a为底，b的对数
*表示乘号，/表示除号
定义式：
若a^n=b(a>0且a≠1)
则n=log(a)(b)
基本性质：
1.a^(log(a)(b))=b
2.log(a)(MN)=log(a)(M)+log(a)(N);
3.log(a)(M/N)=log(a)(M)-log(a)(N);
4.log(a)(M^n)=nlog(a)(M)
推导
1.这个就不用推了吧，直接由定义式可得(把定义式中的[n=log(a)(b)]带入a^n=b)
2.
MN=M*N
由基本性质1(换掉M和N)
a^[log(a)(MN)] = a^[log(a)(M)] * a^[log(a)(N)]
由指数的性质
a^[log(a)(MN)] = a^{[log(a)(M)] + [log(a)(N)]}
又因为指数函数是单调函数，所以
log(a)(MN) = log(a)(M) + log(a)(N)
3.与2类似处理
MN=M/N
由基本性质1(换掉M和N)
a^[log(a)(M/N)] = a^[log(a)(M)] / a^[log(a)(N)]
由指数的性质
a^[log(a)(M/N)] = a^{[log(a)(M)] - [log(a)(N)]}
又因为指数函数是单调函数，所以
log(a)(M/N) = log(a)(M) - log(a)(N)
4.与2类似处理
M^n=M^n
由基本性质1(换掉M)
a^[log(a)(M^n)] = {a^[log(a)(M)]}^n
由指数的性质
a^[log(a)(M^n)] = a^{[log(a)(M)]*n}
又因为指数函数是单调函数，所以
log(a)(M^n)=nlog(a)(M)
其他性质：
性质一：换底公式
log(a)(N)=log(b)(N) / log(b)(a)
推导如下
N = a^[log(a)(N)]
a = b^[log(b)(a)]
综合两式可得
N = {b^[log(b)(a)]}^[log(a)(N)] = b^{[log(a)(N)]*[log(b)(a)]}
又因为N=b^[log(b)(N)]
所以
b^[log(b)(N)] = b^{[log(a)(N)]*[log(b)(a)]}
所以
log(b)(N) = [log(a)(N)]*[log(b)(a)] {这步不明白或有疑问看上面的}
所以log(a)(N)=log(b)(N) / log(b)(a)
性质二：（不知道什么名字）
log(a^n)(b^m)=m/n*[log(a)(b)]
推导如下
由换底公式[lnx是log(e)(x),e称作自然对数的底]
log(a^n)(b^m)=ln(a^n) / ln(b^n)
由基本性质4可得
log(a^n)(b^m) = [n*ln(a)] / [m*ln(b)] = (m/n)*{[ln(a)] / [ln(b)]}
再由换底公式
log(a^n)(b^m)=m/n*[log(a)(b)]
--------------------------------------------（性质及推导 完 ）
公式三:
log(a)(b)=1/log(b)(a)
证明如下:
由换底公式 log(a)(b)=log(b)(b)/log(b)(a) ----取以b为底的对数,log(b)(b)=1
=1/log(b)(a)
还可变形得:
log(a)(b)*log(b)(a)=1
三角函数的和差化积公式
sinα＋sinβ＝2sin（α＋β）/2·cos（α－β）/2
sinα－sinβ＝2cos（α＋β）/2·sin（α－β）/2
cosα＋cosβ＝2cos（α＋β）/2·cos（α－β）/2
cosα－cosβ＝－2sin（α＋β）/2·sin（α－β）/2
三角函数的积化和差公式
sinα ·cosβ＝1/2 [sin（α＋β）＋sin（α－β）]
cosα ·sinβ＝1/2 [sin（α＋β）－sin（α－β）]
cosα ·cosβ＝1/2 [cos（α＋β）＋cos（α－β）]
sinα ·sinβ＝-1/2 [cos（α＋β）－cos（α－β）]
佩服能找资料的啊
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