Prove that $c o t A + t a n A = s e c A . c o s e c A$

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Solution

$L . H . S = c o t A + t a n A$
$= \frac{\cos A}{\sin A} + \frac{\sin A}{\cos A}$
$= \frac{\cos^{2} A + \sin^{2} A}{\sin A . \cos A}$
$= \frac{1}{\sin A . \cos A}$ ……………………. $(\sin^{2} θ + \cos^{2} θ = 1)$
$= \frac{1}{\sin A} . \frac{1}{\cos A}$
$= \cos e c A . s e c A$
$= R . H . S .$
Hence, it is proved that $c o t A + t a n A = s e c A . c o s e c A$

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