一道特殊锐角三角比的值?tan a/2=√3/3求sin²a+(cos a/2)²的值?(要具体步骤)急~

问题描述:

一道特殊锐角三角比的值?
tan a/2=√3/3求sin²a+(cos a/2)²的值?(要具体步骤)急~

由题意可知a/2=30+k180(k整数)解得a=60+360k
sin^2a=√3/2,(cos a/2)²讨论k的取值,当k是奇数时为-√3/2总值为0,当k为偶数时总值为=√3

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