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Question

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

A
1
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B
c/a
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C
a/c
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D
None of these
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Solution

The correct option is D 1
Triangle ABC,A+B+C=180
Cosec A(sinBcosC+cosBsinC)
=cosecA(sin(B+C))
=cosecA(sin(180A))(A+B+C=180)
=CosecA×sinA(sin(180A)=sinA)
(cosecθ=1sinθ)
=1
Option A is correct.

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