证明(3-4cos2A+con4A)/(3+4cos2A+cos4A)=tan^4A

证明(3-4cos2A+con4A)/(3+4cos2A+cos4A)=tan^4A
证明(3-4cos2A+con4A)/(3+4cos2A+cos4A)=tan^4A

证明(3-4cos2A+con4A)/(3+4cos2A+cos4A)=tan^4A
TAN-67
【化学名】(-)-(4aS*,12aR*)-4a-(3-Hydroxyphenyl)-2-methyl-1,2,3,4,4a,5,12,12a-octahydropyrido[3,4-b]acridine
【CAS登记号】【结构式】
【分子式】C23-H24-N2-O
【分子量】344.4556
【原研厂家】Toray (Originator)
【作用类别】ANALGESIC AND ANESTHETIC DRUGS,Analgesic Drugs,Opioid Analgesics,delta-Opioid Agonists
【研发状态】Preclinical
【合成情况】
〖来源〗Chem Pharm Bull
〖合成路线〗
〖标题〗Rational drug design and synthesis of a highly selective nonpeptide delt-opioid agonist,(4aS*,12aR*)-4a-(3-hydroxyphenyl)-2-methyl-1,2,3,4,4a,5,12,12a-octrahydropyrido[3,4-b]acridine (TAN-67)
〖合成方法〗The cyclization of perhydroisoquinoline (I) with o-amino-benzaldehyde (II) in the presence of methanesulfonic acid in refluxing EtOH gave the pyridoacridine (III).Subsequent cleavage of the methyl ether function using n-PrSH and tert-BuOK in boiling DMF provided the target phenol.
〖作者〗Nagase,H.; Kawai,K.; Hayakawa,J.; Wakita,H.; Mizusuna,A.; Matsuura,H.; Tajima,C.; Takezawa,Y.; Endoh,T.
〖参考〗Nagase,H.; Kawai,K.; Hayakawa,J.; Wakita,H.; Mizusuna,A.; Matsuura,H.; Tajima,C.; Takezawa,Y.; Endoh,T.; Rational drug design and synthesis of a highly selective nonpeptide delt-opioid agonist,(4aS*,12aR*)-4a-(3-hydroxyphenyl)-2-methyl-1,2,3,4,4es/10_5_hkavynmfxxnmvbvo.html">eIǚ\x08Ꚑݐul> li>a href="/databases/10_1_vqrupomukvaqu
〖出处〗Chem Pharm Bull1998,46,(11):1695
〖备注〗The cyclization of perhydroisoquinoline (I) with o-amino-benzaldehyde (II) in the presence of methanesulfonic acid in refluxing EtOH gave the pyridoacridine (III).Subsequent cleavage of the methyl ether function using n-PrSH and tert-BuOK in boiling DMF provided the target phenol (1).
〖来源〗Symp Med Chem
〖合成路线〗
〖标题〗Rational drug design and synthesis of opioid delta-receptor selective nonpeptidic agonists - Optical resolution of TAN-67 and the pharmacological effect of each enantiomer
〖合成方法〗The cyclization of perhydroisoquinoline (I) with o-amino-benzaldehyde (II) in the presence of methanesulfonic acid in refluxing EtOH gave the pyridoacridine (III).Subsequent cleavage of the methyl ether function using n-PrSH and tert-BuOK in boiling DMF provided the target phenol.
〖作者〗Fujii,H.; et al.
〖参考〗Fujii,H.; et al.; Rational drug design and synthesis of opioid delta-receptor selective nonpeptidic agonists - Optical resolution of TAN-67 and the pharmacological effect of each enantiomer.Symp Med Chem 1999,Abst 1P-21
〖出处〗Symp Med Chem1999,():Abst 1P-21

3-4cos2A cos4A)/(3 4cos2A cos4A)=(tanA)^4 证明： 由cos2A=2(cosA)^2 - 1 =1-2(sinA)^2 先分析等式左边， 分子（3-4cos2A cos4A） = 3-4[1-2(sinA)^2] [1-2(sin2A)^2] = 8(sinA)^2 - 2(sin2A)^2 = 8(sinA)^2 - 2(2sinAcosA)^2 = 8(...

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3-4cos2A cos4A)/(3 4cos2A cos4A)=(tanA)^4 证明： 由cos2A=2(cosA)^2 - 1 =1-2(sinA)^2 先分析等式左边， 分子（3-4cos2A cos4A） = 3-4[1-2(sinA)^2] [1-2(sin2A)^2] = 8(sinA)^2 - 2(sin2A)^2 = 8(sinA)^2 - 2(2sinAcosA)^2 = 8(sinA)^2 - 8(sinA)^2(cosA)^2 = 8(sinA)^2[1-(cosA)^2] = 8(sinA)^4 分母 (3 4cos2A cos4A) = 3 4[2(cosA)^2 - 1] [2(cos2A)^2 -1] = -2 8(cosA)^2 2(cos2A)^2 = -2 8(cosA)^2 2[2(cosA)^2-1]^2 = 8(cosA)^4 所以，左边 = [8(sinA)^4]/[8(cosA)^4] = (tanA)^4 = 右边 得证。

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