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Principal Solution of Trigonometric Equation

Prove 1-cos...

Question

Prove $\frac{1 - cos A}{1 + cos A} = (csc A - cot A)^{2}$

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Solution

$\frac{1 - cos A}{1 + cos A} \times \frac{1 - cos A}{1 - cos A} = \frac{1 + {cos}^{2} A - 2 cos A}{1 - {cos}^{2} A} = \frac{1 + {cos}^{2} A - 2 cos A}{{sin}^{2} A}$
$= c o s e c^{2} A + {cot}^{2} A - 2 cot A c o s e c A$
$= (c o s e c A - cot A)^{2}$ .

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Principal Solution of Trigonometric Equation

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