Вычислите sina, cosa и tga если tg a/2=2/3

Question

Вычислите sina, cosa и tga если tg a/2=2/3

Answer 1

Cos²(a/2)=1:(1+tg²a/2)=1:(1+4/9)=1:13/9=9/13
cosa=2cos²a/2-1=2*9/13-1=18/13-1=5/13
sina=√(1-cos²a)=√(1-25/169)=12/13
tga=sina/cosa=12/13:5/13=12/13*13/5=12/5=2,4

Answer 2

Sina=(2tga/2)/1+tg^2(a/2)
sina= (2·2/3)/1+(2/3)^2=12/13
cosa=(1-tg^2(a/2))/1+tg^2(a/2)=(1-4/9)/1+4/9=5/13
tga=2tga/2/(1-tg^2a/2)=(2·2/3)/1-4/9=12/5