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If either of the two P, Q and R are equa...

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
(a)`0` (b)`1` (c)`sin(P+Q+R)` (d)`sinQ.sinR`

A

`0`

B

`1`

C

`sin(P+Q+R)`

D

`sinPsinQsinR`

Text Solution

Verified by Experts

The correct Answer is:
A
`(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`
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