Question

已知sina+cosa=17/13,tan a+cot a=?

Answer 1

sina+cosa=17/13
所以(sina+cosa)^2=(17/13)^2
(sina)^2+(cosa)^2+2sinacosa=289/169
1+2sinacosa=289/169
sinacosa=60/169
tana+cota=sina/cosa+cosa/sina
=(sina^2+cosa^2)/sinacosa
=1/(60/169)
=169/60

Answer 2

tan a+cot a=1/cos a*sin a
(sina+cosa)^2=1+2sin a*cos a 推出 sin a*cos a=60/169得出tan a+cot a=1/cos a*sin a=169/60