Question

In a triangle ABC, the value of the expression cosec A (sinB cosC + cosB sinC) is

• A. 1
• B. c/a
• C. a/c
• D. None of these

Answer 1

Answer: (A)

1

Triangle $ABC,\angle A+\angle B+\angle C={180}^{\circ }$

Cosec $A(\sin B\cos C+\cos B\sin C)$

$=\mathrm{cosec}A\left(\sin \right(B+C\left)\right)$

$=\mathrm{cosec}A\left(\sin ({180}^{\circ }-A)\right)(\because A+B+C={180}^{\circ })$

$=\mathrm{Cosec}A\times \sin A(\because \sin ({180}^{\circ }-A)=\sin A)$

$(\because \mathrm{cosec}\theta =\frac{1}{\sin \theta })$

$=1$

Option $A$ is correct.