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JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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In △ABC\triangle A B C, the value of the expression cosec⁡A(sin⁡Bcos⁡C+cos⁡Bsin⁡C)\operatorname{cosec} A(\sin B \cos C+\cos B \sin C) is
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Correct option: A
1
Option A (1) is correct because the expression simplifies to cosec⁡Asin⁡(B+C)=cosec⁡Asin⁡(π−A)=cosec⁡Asin⁡A=1\operatorname{cosec} A \sin(B+C) = \operatorname{cosec} A \sin(\pi - A) = \operatorname{cosec} A \sin A = 1.

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