求证tan(a+π/4)=(1+tana)/(1-tana)

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求证tan(a+π/4)=(1+tana)/(1-tana)

求证tan(a+π/4)=(1+tana)/(1-tana)
求证tan(a+π/4)=(1+tana)/(1-tana)

求证tan(a+π/4)=(1+tana)/(1-tana)
证明:
tan(a+b)=(tana+tanb)/(1-tana·tanb)
∴tan(a+π/4)
=[tana+tan(π/4)]/[1-tana·tan(π/4)]
=(1+tana)/(1-tana)

tan(a+π/4)=(tana+tanπ/4)/(1-tana*tanπ/4)=(1+tana)/(1-tana)
直接用正切的 tan(a+b)=(tana+tanb)/(1-tana*tanb)即可 望采纳

tan(a+π/4)=sin(a+π/4)/cos(a+π/4)=[sinacosπ/4+cosasinπ]/[cosacosπ/4-sinasinπ/4]
分子分母同除以cosacosπ/4得原式=(tana+tanπ/4)/(1-tana*tanπ/4)=(1+tana)/(1-tana)

tan(a+π/4)=(tana+tanπ/4)/(1-tana*tanπ/4);
因为:tanπ/4=1
所以:tan(a+π/4)=(1+tana)/(1-tana)