Question

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Answer 1

$\large\underline{\underline{Question:}}$

$\underline{\underline{Prove:}}$

$\dfrac{1 - tan^{2}\theta}{cot^{2}\theta} = tan^{2}\theta$

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$\large\underline{\underline{To\:Find:}}$

$\text{To Prove that RHS = LHS}$

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$\large\underline{\underline{We\:Know:}}$

$cot\:\theta = \dfrac{1}{tan\:\theta}$

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$\color{red}\large\underline{\underline{Solution:}}$

$\dfrac{1 - tan^{2}\theta}{cot^{2}\theta} = tan^{2}\theta$

$\Rightarrow 1 - tan^{2}\theta = tan^{2}\theta \times (cot^{2}\theta - 1)$

$\Rightarrow 1 - tan^{2}\theta = tan^{2}\theta \times \bigg(\dfrac{1}{tan^{2}\theta} - 1\bigg)$

$\Rightarrow 1 - tan^{2}\theta = 1 - tan^{2}\theta$

$\therefore LHS = RHS$

${\boxed{\therefore \dfrac{1 - tan^{2}\theta}{cot^{2}\theta} = tan^{2}\theta}}$