Question

If A,B,C are the angles of a non right angled triangle ABC. Then find the value of: `|[tanA,1,1],[1,tanB,1],[1,1,tanC]|`

Answer 1

Since the determinant is sysmmetrical it is easier to expand by Sarrus rule. Hence.
`|{:(tanA,,1,,1),(1,,tanB,,1),(1,,1,,tanC):}|`
= tan A tan B tan C +1+1 - tan A -tan B-tan C
=2 [as in a triangle tan A+ tan B + tan C= tan A tan B tan C)