若sina=k+1/k-1,cosa=k-1/k-3,求1/tana的值

题目

若sina=k+1/k-1,cosa=k-1/k-3,求1/tana的值

答案

1/tana=cosa/sina
=[(k-1)/(k-3)] / [(k+1)/(k-1)]
= (k²-1)/(k²-2k-3)