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Introduction

Prove that c...

Question

Prove that
$c o s e c θ (1 + c o s θ) (c o s e c θ - c o t θ) = 1$

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Solution

$L H S = csc θ (1 + cos θ) (csc θ - cot θ) = (csc θ + cot θ) (csc θ - cot θ) = csc^{2} θ - cot^{2} θ = 1 = R H S$

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