Question

prove that :

tan theta - cot theta = 2 sin squared theta - 1 / sin theta cos theta

Answer 1

Answer:

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Answer 2

$\text{\huge{Question}}$

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

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$\text{\huge{Solution}}$

$\text{Taking LHS}$



$tan\theta - cot\theta \\ \\ = > \frac{sin\theta }{cos\theta} - \frac{cos\theta}{sin\theta} \\ \\ = > \frac{ {sin}^{2}\theta - {cos}^{2}\theta }{sin\theta \: cos\theta}$

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$\text{As we know that}$

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

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$= > \frac{{sin}^{2} \theta - ( 1 - {sin}^{2} \theta)}{sin\theta \: cos\theta} \\ \\ = > \frac{{sin}^{2} \theta -1 + {sin}^{2} \theta}{sin\theta \: cos\theta} \\ \\ = > \frac{2{sin}^{2} \theta - 1}{sin\theta \: cos\theta}$

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


$\text{HENCE PROVED}$

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$\text{\huge{Thanks}}$