Question

tan theta - cot theta
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Answer 1

$\mapsto \LARGE \color{aqua}\mathbb {QUESTION} :$

tan theta - cot theta

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We know that,

$\LARGE \boxed{ \tan \theta \: = \frac{sin \theta}{cos \theta} }$

$\LARGE \boxed{cot \theta \: = \frac{cos \theta}{sin \theta} }$

Now tan theta - cot theta ,

$\large \mathtt{tan \theta - cot \theta \: = \frac{sin \theta}{cos \theta} - \frac{cos \theta}{sin \theta} }$

$\LARGE = \frac{ {sin \theta \: }^ {2} - {cos \theta \: }^{2} }{cos \theta sin \theta}$

Now we know that,

=> sin^2 theta = 1 - cos ^ 2 theta

$\LARGE = \frac{ 1 - {cos}^{2} \theta - {cos}^{2} \theta}{cos \theta \:sin \theta}$

$= \LARGE \color{aqua} \frac{ 1 \: - \: 2 \: {cos}^{2} \theta \: }{cos \theta \: sin \theta}$

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hope it helps....