已知tana=1/2求下列各式的值 sin^2a+sina*cosa+2

tan(a)=1/2
sin²(a)+sin(a)*cos(a)+2
=cos²(a)*[tan²(a)+tan(a)]+2
=cos²(a)*(3/4)+2
=1/[1/cos²(a)]*(3/4)+2
=1/{[sin²(a)+cos²(a)]/cos²(a)}*(3/4)+2
=1/[tan²(a)+1]*(3/4)+2
=1/(1/4+1)*(3/4)+2
=(4/5)*(3/4)+2
=3/5+2
=13/5