tana=3tan(a b),b=π 6,求sin(2a b)的值

2a+b=(a+b)+ab=(a+b)-a为了简单设x=a+b3cos(2a+b)+5cosb=3cosxcosa-3sinxsina+5cosxcosa+5sinxsina=8cosxcosa+2s

右边=tan(a+b)[1-tana*tanb]=[(tana+tanb)/(1-tana*tanb)]/[1-tana*tanb]=tana+tanb=左边

5sinB=sin(2A+B)=sin(A+B+A)=sin(A+B)cosA+cos(A+B)sinA,sinB=sin(A+B-A)=sin(A+B)cosA-cos(A+B)sinA5sin(A

2A+B=(A+B)+A,B=(A+B)-A,所以由SIN(2A+B)=3SINB得sin(A+B)cosA＋cos(A+B)sinA＝3sin(A+B)cosA-3cos(A+B)sinA2sin(

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

3sinb=sin(2a+b)可得sin(2a+b)-sinb=2sinb由两角正弦差的公式：sin(2a+b)-sinb=2cos[(2a+b+b)/2]sin[(2a+b-b)/2]=2cos(a

tan(A+B)=2tanAsin(A+B)*cosA=2sinA*cos(A+B)①sin(A+B)*cosA-sinA*cos(A+B)=sinA*cos(A+B)sinB=sinA*cos(A+

由tan(A+B)=3tanA可以得到：sin(A+B)cosA=3sinAcos(A+B)展开,得(sinAcosB+cosAsinB)*cosA=3sinA*(cosAcosB-sinAsinB)

结果:tana*tanb=1/2.过程也不复杂,把tana移项,然后展开tan(a+b),再全部通分,两边合并同类项.

tan(A+B)=tan(π-C)=tanC=1C=π/4,或C=3π/4tanA=tan[(A+B)-B]=[tan(A+B)-tanB]/[1+tan(A+B)*tanB]=1/2tanB

(tanA+tanB)/(1-tanA*tanB)=-1两边同乘以(1-tanA*tanB),等式两边就为(tanA+tanB)=-(1-tanA*tanB),“-“(1-tanA*tanB)注意这个

不相等,正确的式子应该是tan(A+B)=tanA+tanB+tanAtanBtan(A+B)推倒的方式如下：∵tan(A+B)=(tanA+tanB)/(1-tanAtanB)tanA+tanB=(

左边=(tana-tanb)/(-1/tana+cotb)=(tana-tanb)/(-1/tana+1/tanb)上下乘tanatanb=tanatanb(tana-tanb)/(tana-tanb

3sinB=sin(2A+B)3sin(A+B-A)=sin(A+b+A)3sin(A+B)cosA-3cos(A+b)sinA=sin(A+B)cosA+sinAcos(a+b)2sin(A+b)c

3sinb=sin(2a+b)3sin(a+b-a)=sin(a+b+a)3[sin(a+b)cosa-cos(a+b)sina]=sin(a+b)cosa+cos(a+b)sinasin(a+b)c

3sinB=sin(2A+B)3sin(A+B-A)=sin(A+B+A)3sin(A+B)cosA-3cos(A+B)sinA=sin(A+B)cosA+sinAcos(A+B)2sin(A+B)c

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

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)=(tana+tanb)/(1-tanatanb)=(2/5+3/7)/(1-2/5*3/7)=(14/35+15/35)/(1-6/35)=(29/35)/(29/35)=1tan(

sin(α+β+α)=3sin(α+β-α)sin(α+β)cosα+cos(α+β)sinα=3sin(α+β)cosα-3cos(α+β)sinα4cos(α+β)sinα=2sin(α+β)co