已知tana=1/2,求sin²a+sinacosa+2的值

已知tana=1/2,求sin²a+sinacosa+2的值
已知tana=1/2,求sin²a+sinacosa+2的值

已知tana=1/2,求sin²a+sinacosa+2的值
sin²a+sinacosa+2=（sin²a+sinacosa）/(sin²a+cos²a)+2
=(tan²a+tana)/(tan²a+1)+2
=(3/4)/(5/4)+2
=3/5+2
=13/5

tana=1/2=sina/cosa
cosa=2sina
sin²a+cos²a=1=5sin²a
sin²a=0.2
sin²a+sinacosa+2=sin²a+2sin²a+2=2+3sin²a=2.6