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The expression sinθ/(1 + cosθ) + (1 + cosθ)/sinθ simplifies to:

Competition practiceTrigonometry

A2 secθ
B2 cosecθ
Ccosecθ
D2 cotθ

Step-by-Step Solution

The numerator becomes si

n^{2}

θ +

(1 + cos θ)^{2} = 2 + 2

cosθ = 2(1 + cosθ); dividing by sinθ(1 + cosθ) leaves 2/sinθ = 2 cosecθ.

Answer: B) 2 cosecθ

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