Question

prove that sec a - cosec a 1 +tan a +cot a = tan a sec a - cot a cosec a

Answer 1

Hey, here is your answer...

$need \: to \: prove... \\ \\ \sec( \alpha ) - \csc( \alpha ) + \tan( \alpha ) + \cot( \alpha ) = \tan( \alpha ) \sec( \alpha ) - \cot( \alpha ) \csc( \alpha ) .... \\ \\ \\ = > \: \sec( \alpha ) - \csc( \alpha ) + \tan( \alpha ) + \cot( \alpha) \\ = > \: (1 \div \cos( \alpha )) - (1 \div \sin( \alpha )) + \tan( \alpha ) + (1 \div \tan( \alpha )) \\ = > \: (1 \div \cos( \alpha )) - (1 \div \sin( \alpha )) + ( ((\sin( \alpha )) \div ( \cos( \alpha ))) + (( (\cos( \alpha )) \div ( \sin( \alpha ))) \\ = > \: (( \sin( \alpha ) + 1) \div ( \cos( \alpha ))) + (( \cos( \alpha ) - 1) \div ( \sin( \alpha ))) \\ = > \: ((( \sin( \alpha ) + 1) ( \sin( \alpha )) + ((( \cos( \alpha ) - 1)( \cos( \alpha ))) \div ( \sin( \alpha ) \cos( \alpha )) \\ = > \: ( \sin( \alpha ) + { \sin }^{2}( \alpha ) + { \cos }^{2}( \alpha ) - \cos( \alpha )) \div ( \sin( \alpha ) \cos( \alpha )) \\ = > \: (1 + \sin( \alpha ) - \cos( \alpha )) \div ( \sin( \alpha ) \cos( \alpha )) \\ = > \: (csc( \alpha ) \sec( \alpha ) + \sec( \alpha ) - \csc( \alpha )) \\ = > ( \tan( \alpha ) \sec( \alpha ) - \cot( \alpha ) \csc( \alpha )) \\ \\ \\ \\ \\ hence \: proved... \\ \\ \\ hope \: this \: helps \: you.. \\ thank \: you.. \\ \\ plzz \: mark \: me \: as \: brainliest.....$

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Answer 2

Answer:

Hope it helps you friend.