sin²a+(cos a/2)²
=sin²a+(cos a+1)/2
=[(2tana/2)/(1+tana/2^2)]^2+[(1+tana/2^2)/(1-tana/2^2)]/2+1/2
=[(2*√3/3)/(1+1/3)]^2+[(1-1/3)/(1+1/3)]/2+1/2
=(√3/2)^2+(1/2)/2+1/2
=3/4+3/4
=3/2
sin²a+(cos a/2)²
=sin²a+(cos a+1)/2
=[(2tana/2)/(1+tana/2^2)]^2+[(1+tana/2^2)/(1-tana/2^2)]/2+1/2
=[(2*√3/3)/(1+1/3)]^2+[(1-1/3)/(1+1/3)]/2+1/2
=(√3/2)^2+(1/2)/2+1/2
=3/4+3/4
=3/2