作者G41271 (茶)
看板trans_math
标题Re: [积分] 有关以切表弦的东西
时间Sat Apr 11 13:59:28 2009
sin(A+B)= sinAcosB + cosAsinB,
(sin cos的和角公式,我假设你知道,希望没假设错)
cos(A+B)= cosAcosB - sinAsinB,
sin(A+B) sinAcosB + cosAsinB
tan(A+B)= --------- = ---------------------- 然後分子分母同除cosA,cosB
cos(A+B) cosAcosB - sinAsinB
tanA + tanB
所以tan(A+B) = -------------- (sinx/cosx = tanx)
1-tanAtanB
2tanx
令A=B=x,代入可得 tan2x = ----------- , 同样的,代入sin,cos的和角公式:
1- (tanx)^2
2sinx/cosx 2tanx 2tanx
sin2x = 2sinxcosx = -------------- = --------- = ----------
(1/cosx)^2 (secx)^2 1+(tanx)^2
1- [(sinx)^2/(cosx)^2]
cos2x = (cosx)^2 - (sinx)^2 = ------------------------
(1/cosx)^2
1- (tanx)^2 1- (tanx)^2
= --------------- = -------------
(secx)^2 1+ (tanx)^2
(同样的,我假设你已经知道1/cosx = secx 和 1+(tanx)^2 = (secx)^2 .)
(参考资料: 高一下数学课本)
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◆ From: 123.204.160.16
※ 编辑: G41271 来自: 123.204.160.16 (04/11 14:02)
1F:推 Frobenius:推~ 118.161.244.47 04/11 15:52
2F:推 tcpetcpe:推 很详尽 很感谢 你说的那些我都知道210.240.176.170 04/11 20:58
3F:→ tcpetcpe:原来是同除cosacosb 很感谢!!!!210.240.176.170 04/11 20:59
4F:→ tcpetcpe:忘记了 科科210.240.176.170 04/11 20:59
5F:→ condensed:值得一推 123.204.16.185 04/11 21:51