Q71 / 180 · COMEDK 2015 · Mathematics

In a $\triangle A B C, \operatorname{cosec} A(\sin B \cos C+\cos B \sin C)=$

  • A
    0
  • Correct answer
    B
    1
  • C
    $-1$
  • D
    None of these

Solution

$\operatorname{cosec} A(\sin B \cos C+\cos B \sin C)$ $$ \begin{aligned} &=\operatorname{cosec} A \sin (B+C) \\ &=\operatorname{cosec} A \sin \left(180^{\circ}-A\right) \\ &\quad[\because A, B \text { and } C \text { are angles of a triangle }] \\ &=\frac{1}{\sin A} \sin A=1 \end{aligned} $$

Hence, the correct answer is option: 'B'.

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