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The value of the determinant |[2, tanAco...

The value of the determinant `|[2, tanAcotB+cotAtanB, tanAcotC+cotAtanC] , [tanBcotA+cotBtanA, 2, tanBcotC+cotBtanC] , [tanCcotA+cotCtanA, tanCcotB+cotCtanB,2]|` is

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Without expanding at any stage, evaluate the value of the determinant |{:(2,tanAcot B+cotAtanB,tanAcotC+cotAtanC),(tanBcotA+cotBtanA,2,tanBcotC+cotBtanC),(tanCcotA+cotCtanA,tanBcotC+cotBtanC,2):}|.

Without expanding at any stage, evaluate the value of the determinant |{:(2,tanAcot B+cotAtanB,tanAcotC+cotAtanC),(tanBcotA+cotBtanA,2,tanBcotC+cotBtanC),(tanCcotA+cotCtanA,tanBcotC+cotBtanC,2):}|.

Without expanding at any stage, evaluate the value of the determinant |{:(2,tanAcot B+cotAtanB,tanAcotC+cotAtanC),(tanBcotA+cotBtanA,2,tanBcotC+cotBtanC),(tanCcotA+cotCtanA,tanBcotC+cotBtanC,2):}|.

Without expanding at any stage, evaluate the value of the determinant |{:(2,tanAcot B+cotAtanB,tanAcotC+cotAtanC),(tanBcotA+cotBtanA,2,tanBcotC+cotBtanC),(tanCcotA+cotCtanA,tanBcotC+cotBtanC,2):}|.

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