Question

prove that .tan Q(1-cot Q) +cot Q(1-tan Q) =1+sec Q(cosecQ ).
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Answer 1

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Prove that. tan/1-cot+cot/1-tan=(1+sec cosec)

Prove that. tan/1-cot+cot/1-tan=(1+sec cosec)

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Answer 2

$\huge\underline\mathfrak\red{ANSWER}$

$\tan \alpha (1 - \cot \alpha ) + \cot \alpha (1 - \tan \alpha ) \\ \\ \tan \alpha (1 - \frac{1}{ \tan \alpha } ) + \cot \alpha ( 1 - \frac{1}{\cot \alpha } ) \\ \\ ( \tan\alpha - 1) + ( \cot \alpha - 1) \\ \\ ( \tan \alpha + \cot \alpha ) - 2 \\ \\ ( \frac{1}{ \cot \alpha } + \cot \alpha ) - 2 \\ \\ (\frac{1 + {cot}^{2} \alpha }{ \cot \alpha } ) - 2 \\ \\ \frac{ {cosec}^{2} \alpha }{ \cot \alpha } - 2 \\ \\ {cosec}^{2} . \frac{ \sin \alpha }{ \cos \alpha } - 2 \\ \\ \frac{cosec \alpha }{ \cos \alpha } - 2 \\ \\ \sec \alpha .cosec \alpha - 2$

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