已知tana=2 (1)求tan(2a π 4)

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tan(a-π/4)=(tana-tanπ/4)/（1+tana*tanπ/4）=（2-1）/（1+2*1）=2/3

sin(2A+B)=sin(2A)cosB+cos(2A)sinB,sin(2A)=2tanA/(1+tanA^2)=1,cos(2A)=(1-tanA^2)/(1+tanA^2)=0,则由sin(2

tan(π/4+A)=sin(π/4+A)/cos(π/4+A)=(sinπ/4*cosA+cosπ/4*sinA)/(cosπ/4*cosA-sinπ/4*sinA)=(tanπ/4*cosA+si

因为tanb＝1/3所以tan（2b）＝2tanb/（1－tanbtanb）＝3/4,所以tan（a＋2b）＝（tana＋tan2b）/（1－tanatan2b）,将tana＝1/7和tan2b＝3/

tan4/派=1所以tan(a+4/派)=(1-tanatan4/派)/(tana+tan4/派)=(1-tana)/(tana+1)=2/12tana+2=1-tanatana=-3/1

tanA:tanB:tanC=1:2:3→tanA:tanB:tan【π-（A+B)】=1:2:3→tanA:tanB:—tan（A+B)=1:2:3,3tanA=—tan(A+B)=—(tanA+t

tan(A-B)=(tanA-tanB)/(1+tanA*tanB)tan(A-B)/tanA+sin²C/sin²A=1左右移项得1-[(tanA-tanB)/(1+tanA*t

(tanA-根3)（tanA-1）=0tanA=根3或tanA=1A=60度或A=45度

tan(a+β)=7(tana+tanβ)/(1-tanatanβ)=73(tana+tanβ)=73sin(a+β)/cosacosβ=7cosacosβ=3sin(a+β)/7=3(7/5√2)/

1.∵tan(a/2)=2∴tana=[2tan(a/2)]/{1-[tan(a/2)]^2}=(2×2)/(1-2^2)=-4/3∴tan(a+π/4)=[tana+tan(π/4)]/[1-tan

tana+1/tana=3可化成sina/cosa+cosa/sina=3化简得sin^2a+cos^2a/sinacosa=3可得出sinacosa=1/3由此可得出sina+cosa=根号15/3

3*sin(a+b-a)=sin(a+b+a);3*sin(a+b)cos(a)-3*cos(a+b)sin(a)=sin(a+b)cos(a)+cos(a+b)sin(a);2*sin(a+b)co

tan3a=[3tana-(tana)^3]/[1-3(tana)^2]=1/tana,∴3(tana)^2-(tana)^4=1-3(tana)^2,∴(tana)^4-6(tana)^2+1=0,

tan(a+2b)=(tana+tan2b)/(1-tanatan2b)tan2b=2tanb/(1-tan^2b)tana=1/7,tanb=1/3带入tan2b=2tanb/(1-tan^2b)=

tana=1a=kπ+π/43sinB=sin(2a+B)=sin(2kπ+π/2+B)=cosB3sinB=cosBsin^2B+cos^2B=1cos^2B=9/10sin^2B=1/10sinB

tan(a+b)=(-7-3)/(21-1)=-1/2tan(2a+b)=[tana+tan(a+b)]/[1-tana*tan(a+b)]=(-2-3)/(6-1)=-1

∵tanA-1/tanA=2∴平方,tan²A-2+1/tan²A=4∴tan²A+1/tan²A=6

tan(45'+a)=(tan45'+tana)/(1-tan45'tana)=(1+tana)/(1-tana)=1/22+2tana=1-tanatana=-1/3tana=sina/cosa=-

tan周期是π所以tan(π+a)=tana=-1/2sina/cosa=tana=-1/2cosa=-2sina代入(sina)^2+(cosa)^2=15(sina)^2=1(sina)^2=1/