Question

tan theta+ cot theta= sec theta × cosec theta​

Answer 1

Step-by-step explanation:

$\tan( \alpha ) + \cot( \alpha ) = \sec( \alpha ) \csc( \alpha ) \\ \\ \\ \tan( \alpha ) + \cot( \alpha ) \\ \\ \\ = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } + \frac{ \cos( \alpha ) }{ \sin( \alpha ) } \\ \\ \\ = \frac{ { \sin }^{2} \alpha + { \cos }^{2} \alpha }{ \sin( \alpha) \cos( \alpha ) } \\ \\ \\ = \frac{1}{ \sin( \alpha ) \cos( \alpha ) } \\ \\ \\ = \sec( \alpha )\csc( \alpha) \\ \\ \\ hence \: proved$

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