For any `triangleABC`, the value of determinant `|[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,cotC,1]|` is:

Explanation

Given,`|[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,cotC,1]|`

det along `C_3`

​=`1(sin^2BcotC−sin^2CcotB)−sin^2AcotC+sin^2CcotA+sin^2AcotB−cotAsin^2B`

A triangle meant it can even be an equilateral triangle


⇒A=B=C=60^@

`|[3/4,1/sqrt(3),1],[3/4,1/sqrt(3),1],[3/4,1/sqrt(3),1]|`

=`sqrt(3)/4[[1,1,1],[1,1,1],[1,1,1]]`

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