已知tana= 3计算14sin-2cos 5cos 3sin

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

由已知条件得：tana=1/2(1)分子分母同除以cosa原式=-5/3(2）原式=3sina*cosa+2=3sina*cosa/(sina*sina+cosa*cosa)=16/5好好学习孩子!

因为tana=2sina/cosa=2,sin^2a+cos^2a=1所以sina=2跟号5/5,cosa=跟号5/51.原式＝-2sina-(-cosa)/cosa+3sina=sina+1=2根号

sin2a=2tana/[1+(tana)^2]=2*1/[1+1]=1(cos2a)^2=1-(sin2a)^2(cos2a)^2=1-1(cos2a)^2=0cos2a=03sinB=sin(2a

由tana=0.5得sin2a=2*0.5/(0.5^2+1)=4/5cos2a=(1-0.5^2)/(1+0.5^2)=3/5sin(2a+b)=sin2a*cosb+cos2a*sinb=4/5c

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

sina/cosa=tana=3sina=3cosasin²a=9cos²a因为sin²a+cos²a=1所以cos²a=1/10所以sina

tana=3所以sina平方=(3/√(3^2+1)]^2=9/10sincos=3/√10*1/√10=3/10sin平方-sincos=9/10-3/10=3/5

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

因为：tana=1,所以a=pai/4+k*pai又因为：3sinb=sin[2(pai/4+k*pai)+b]=sin(pai/2+2k*pai+b)=sin(pai/2+b)=cosb所以：tan

解:因为tana/(tana-1)=-1,所以tana=1/2,所以[sin(PAI-a)＋3cos(PAI＋a)]/[sina＋cos(-a)]=(sina＋3cosa)/(sina＋cosa)=(

（tana-tanb）/（tana+tanb）=（sina/cosa-sinb/cosb）/（sina/cosa+sinb/cosb）=(sinacosb-cosasinb)/(sinacosb+co

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

3sinacosa=3sinacosa/（sin²a+cos²a）分子分母同时除以cos²a得原式=3tana/（tan²a+1）=-12/17再问：那个同时除

sin²a-sinacosa=sinacosa(tana-1)=cos²atana(tana-1)又sin²a+cos²a=cos²a(tan

(1+tana)/(1-tana)=-1+2/(1-tana)=3+√21/(1-tana)=2+√21-tana=(2-√2)/2tana=√2/2sina/cosa=√2/2(sina)^2/(c

(1+tana)/(1-tana)=3+2√2化简求得tana=(根号2)/2所以cosa=2/根号6sina=（根号2）/(根号6)cos(π-a)方+sin(π+a)cos(π-a)+sin(a-

sin^2a-3sinacosa+cos^2a=(sin^2a-3sinacosa+cos^2a)/(sin^2a+cos^2a)=(tan^2a-3tana+1)/(tan^2a+1)=(3^2-3

sin²a+2sinacosa+1=sin²a+2sinacosa+sin²a+cos²a=(2sin²a+2sinacosa+cos²a)