If either of the two `P`, `Q` and `R` are equal and `P+Q+R=180^(@)`, then the value of `|{:(1, 1+sinP,sinP(1+sinP)),(1,1+sinQ,sinQ(1+sinQ)),(1,1+sinR,sinR(1+sinR)):}|` is

Options

A. `0`
B. `1`
C. `sin(P+Q+R)`
D. `sinPsinQsinR`

Answer

A

Explanation

`(a)` Applying `C_(2)toC_(2)-C_(1)` and then `C_(3)toC_(3)-C_(2)`
`Delta=|{:(1,sinP,sin^(2)P),(1,sinQ,sin^(2)Q),(1,sinR,sin^(2)Q):}|=(sinP-sinQ)(sinQ-sinP)`
`(sinR-sinP)`
`impliesDelta=0`