sin a+cos a=17/13,则tan a+ cot a=

显示全部楼层 · 2011-6-18 16:14:23

sin a+cos a=17/13(sin a+cos a)^2=(17/13)^2=289/169=1+2sinacosasinacosa=60/16960/169=sinacosa/1=sinacosa/(sin^2a+cos^2a)=tana/(tan^2+1)60tan^2+169tana+60=0(12tana+5)(5tana+12)=0tana=-12/5或tana=-5/12，当tana=-12/5时tan a+ cot a=-24/5当tana=-5/12时tan a+ cot a=＝-5/6...

千问 · 2011-6-18 16:14:23

sin a+cos a=17/13平方得 1+2sinacosa=289/169，sinacosa=60/169所以 tana+cota
=sina/cosa+cosa/sina
=1/(sinacosa)
=169/60...

千问 · 2011-6-18 16:14:23

楼上算错了，sin a+cos a=17/13，两边平方得，1+2sin acos a=289/169
可以得到sin acos a=60/169tan a+ cot a=sin a/cos a+cos a/sina通分得
=1/sinacosa=169/60...

千问 · 2011-6-18 16:14:23

tan a+ cot a=sina/cosa+cosa/sina=1/sina×cosasin a+cos a=17/13两边平方得：1+2sina×cosa=289/169 后面自己做...