# In a $\Delta ABC$ the value of the expression $cosec A(\sin B\cos C+\cos B\sin C)$ is

$(a)\;1\qquad(b)\;\large\frac{c}{a}$$\qquad(c)\;\large\frac{a}{c}\qquad$$(d)\;None\;of\;these$

Given expression =$cosec A(\sin B\cos C+\cos B\sin C)$
$\sin(B+C)=\sin B\cos C+\cos B\sin C$
$\Rightarrow cosec A(\sin(B+C)$
$\Rightarrow cosec A\sin(\pi-A)$
Since $A+B+C=\pi$
$\Rightarrow cosec A.\sin A$
$\Rightarrow 1$
Hence (a) is the correct option.
answered Oct 9, 2013