已知tana=-1/2,求1+2sinacosa/sin²a-cos²a的值是

题目

已知tana=-1/2,求1+2sinacosa/sin²a-cos²a的值是
A.1/3 B.3 C.-1/3 D.-3
有过程最好,3Q

答案

1+2sinacosa/sin²a-cos²a
=sin²a+cos²a+2sinacosa/sin²a-cos²a
=tan²a+1+2tana/(tan²a-1)
=[1/4+1-1]/(1/4-1)
=(1/4)/(-3/4)
=-1/3
选C