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Standard Values of Trigonometric Ratios

Prove that : ...

Question

Prove that :
$cot A - tan A = \frac{2 {cos}^{2} A - 1}{sin A cos A}$

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Solution

$cot A - tan A$
$= \frac{cos A}{sin A} - \frac{sin A}{cos A}$
$= \frac{{cos}^{2} A - {sin}^{2} A}{sin A cos A}$
$= \frac{{cos}^{2} A - (1 - {cos}^{2} A)}{sin A cos A}$
$= \frac{2 {cos}^{2} A - 1}{sin A cos A}$

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Similar questions

tan A - cot A = \frac{1 - 2 {cos}^{2} A}{sin A cos A}

\frac{tan A}{(1 + {tan}^{2} A)^{2}} + \frac{cot A}{(1 + {cot}^{2} A)^{2}} = sin A cos A

\frac{t a n A}{(1 + t a n^{2} A)^{2}} + \frac{c o t A}{(1 + c o t^{2} A)^{2}} = s i n A c o s A

tan A = \sqrt{2} - 1

, then prove that

sin A cos A = \frac{1}{2 \sqrt{2}}

\frac{tan A}{(1 + {tan}^{2} A)^{2}} + \frac{cot A}{(1 + {cot}^{2} A)^{2}} = sin A cos A

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