Question

In a $\Delta ABC, cosec\, A(\sin\, B \, \cos\, C + \cos \, B\, \sin\, C)$ =

• A. $0$
• B. $1$
• C. $-1$
• D. $None\, of\, these$

Answer 1

Answer: (B)

$1$

Answer 2

$cosec\, A(\sin\, B \, \cos\, C + \cos \, B\, \sin\, C)$
$= cosec \, A \, \sin\, (B + C)$
$= cosec\, A \, \sin (180? - A)$
[ $\because \, A, B$ and $C$ are angles of a triangle]
$= \frac{1}{\sin \, A} \sin \, A = 1$