Question

tan/1-cot+cot/1-tan=1+sec×cosec​

Answer 1

ANSWER.....

$\frac{tan \alpha }{1 - \cot \alpha } + \frac{cot \alpha }{1 - tan \alpha } \\ \\ \frac{ \frac{ \sin \alpha }{ \cos \alpha } }{ \frac{ \sin \alpha - \cos \alpha }{ \sin \alpha } } + \frac{ \frac{ \cos \alpha }{ \sin \alpha } }{ \frac{ \cos \alpha - \sin \alpha }{ \cos( \alpha ) } } \\ \\ \frac{ {sin}^{2} \alpha }{ \cos \alpha ( \sin \alpha - \cos \alpha ) } + \frac{ {cos}^{2} \alpha }{ \sin \alpha ( \cos \alpha - \sin \alpha ) } \\ \\ \frac{ {sin}^{3} \alpha - {cos}^{3} \alpha }{ \cos \alpha \sin \alpha {(sin \alpha - \cos \alpha ) } } \\ \\ \frac{( \sin \alpha - \cos \alpha )( {sin}^{2} \alpha + {cos}^{2} \alpha + \sin \alpha \cos \alpha ) }{ \cos\alpha \sin \alpha {( \sin \alpha - \cos \alpha ) } } \\ \\ \frac{1 + \cos\alpha \sin \alpha }{ \: \cos \alpha \sin \alpha } \\ \\ \frac{1}{ \cos\alpha \sin \alpha } + \frac{ \cos\alpha \sin \alpha }{ \sin \alpha \cos \alpha } \\ \\ \sec \alpha \csc \alpha + 1$

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