In a triangle `ABC`, if `a,b,c` are the sides opposite to angles `A`, `B`, `C` respectively, then the value of `|{:(bcosC,a,c cosB),(c cosA,b,acosC),(acosB,c,bcosA):}|` is
A. `1`
B. `-1`
C. `0`
D. `acosA+bcosB+c cosC`
Correct Answer - B
`(b)` Let `Delta=|{:(sinA,1,1),(1,sinB,1),(1,1,sinC):}|`
Apply `C_(2)toC_(2)-C_(1)` and `C_(3)toC_(3)-C_(1)`
Then expand along `C_(1)`, we get
`Delta=sinA(1-sinB)(1-sinC)+(1-sinA)(1-sinB)+(1-sinA)(1-sinC)`
Since `A,B,C` are angles of a triangle, `0 lt sin A, sinB,sinC le...