已知sina+cosa=1/3,求tan^2 a+cot^2 a的值.
问题描述：
已知sina+cosa=1/3,求tan^2 a+cot^2 a的值.
答
sina+cosa=1/3
sin^2a+2sinacosa+cos^2a=1/9
sin2a=-8/9
tan^2 a+cot^2 a=sin^2a/cos^2a+cos^2a/sin^2a
=(sin^4a+cos^4a)/(sinacosa)^2
=[(sin^2a+cos^2a)^2-2sin^2acos^2a)/(sinacosa)^2
=4/(2sinacosa)^2-2
=4*(-9/8)^2-2=49/16