tana+1/tana=9/4,则tan^2+1/sinacosa+1/tan^2a=?

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tana+1/tana=9/4,则tan^2+1/sinacosa+1/tan^2a=?tana+1/tana=9/4,则tan^2+1/sinacosa+1/tan^2a=?tana+1/tana=

tana+1/tana=9/4,则tan^2+1/sinacosa+1/tan^2a=?
tana+1/tana=9/4,则tan^2+1/sinacosa+1/tan^2a=?

tana+1/tana=9/4,则tan^2+1/sinacosa+1/tan^2a=?
sina/cosa+cosa/sina=9/4=1/sinacosa ,(sinacosa)^2=16/81
tan^2+1/sinacosa+1/tan^2a=sin^2a/cos^2a+9/4+cos^2a/sin^2a
=9/4+(sin^4a+cos^4a)/sin^2acos^2a
=9/4+[(sin^2a+cos^2a)^2-2(sinacosa)^2]/(sinacosa)^2
=9/4+(1-32/81)81/16
=9/4+49/16=85/16