tanA+cotA=3,A是锐角,求tan^A+cot^A=?

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tanA+cotA=3,A是锐角,求tan^A+cot^A=?

tanA+cotA=3,A是锐角,求tan^A+cot^A=?
tanA+cotA=3,A是锐角,求tan^A+cot^A=?

tanA+cotA=3,A是锐角,求tan^A+cot^A=?
锐角,tanA>0
(tanA+1/tanA)^2=3*3=9
tan^A+1/tan^A+2=9
tan^A+cot^A=tan^A+1/tan^A=7

tan^A+cot^A=tan^A+cot^A+2-2=(tanA+cotA)^-2=9-2=7