a属于(0,pai/2) tana=1/2 求tan2a和sin(2a+pai/3)的值

a属于(0,pai/2) tana=1/2 求tan2a和sin(2a+pai/3)的值
a属于(0,pai/2) tana=1/2 求tan2a和sin(2a+pai/3)的值

a属于(0,pai/2) tana=1/2 求tan2a和sin(2a+pai/3)的值
a∈(0,π/2),tana=1/2,则tan2a=[2tana]/[1－tan²a]=4/3；sin(2a＋π/3)=(1/2)sin2a＋(√3/2)cos2a.sin2a=[2tana]/[1＋tan²a]=4/5,cos2a=[1－tan²a]/[1＋tan²a]=3/5,则sin(2a＋π/3)=(4＋3√3)/10

tan2a=2tana/(1-tan^a)=4/3
sin(2a+pai/3)
=1/2*sin2a+√3/2*cos2a
=sinacosa+√3/2*(2cos^a-1)
根据tana=1/2,构成直角三角形
sina=1/√5
cosa=2/√5代入
=2/5+3√3/10
希望能帮到你，祝学习进步O(∩_∩)O,也别忘了采纳！

易得a小于45度，则2a小于90度。
tan2a=[2tana]/[1－tan²a]=4/3；sin(2a＋π/3)=(1/2)sin2a＋(√3/2)cos2a。sin2a=[2tana]/[1＋tan²a]=4/5，cos2a=[1－tan²a]/[1＋tan²a]=3/5，则sin(2a＋π/3)=(4＋3√3)/10

tan2a=2tana/(1-(tana)^2)=1/(1-1/4)=4/3
tana=sina/cosa=1/2
cosa=2sina
(sina)^2+ (cosa)^2=1
(sina)^2=1/5
a属于(0,pai/2),故有sina=根号5/5,cosa=2根号5/5
故sin2a=2sinacosa=2*2/5=4/5,cos2a=1-2(sina)^2=1-2/5=3/5
sin(2a+pai/3)=sin2acospai/3+cos2asinpai/3=4/5*1/2+3/5*根号3/2=(4+3根号3)/10

tan2a=2tana/(1-tan^2a)=2*1/2 / (1-1/4)=4/3
tana=1/2<1
a∈(0,π/4)
2a∈(0,π/2)
sin2a=4/5
cos2a=3/5
sin(2a+π/3)=sin2a*cosπ/3+sinπ/3*cos2a=4/5 *1/2+√3/2 * 3/5=(3√3+4)/10

,(2√5/5-cosa)(√5/5-cosa)=0 , cosa= 2√5/5 sina=√5/5 , tana=1/2 tan2a=2tana/(1-tan^2a)=1/(1-1/4)=4/3

tan2a=2tana/(1+tana*tana)=4/5
sin(2a+pai/3)=sin2a*cospai/3+cos2a*sinpai/3
sin2a=2sinacosa
cos2a=2cosacosa-1
通过画直角三角形求sina cosa
或tana=0.5 sinasina+cosacosa=1
求sina cosa 当然sina》0 cosa》0