Question

If tanA +cotA = 2 prove that tancubeA +cot cube A= 2

Answer 1

$\tan(a) + \cot(a) = 2 \\ \tan^{3} (a) + \cot^{3} (a) = ( \tan(a) + \cot(a) ) \\ ( \tan^{2} (a) - \tan(a) \cot(a) + \cot^{2} (a) ) \\ = 2( ({ \tan(a) + \cot(a) ) }^{2} - 3 \tan(a) \cot(a) ) \\put \: the \: value \: and \: tan \: cot \: cancels \: each \: other \\ = 2( {2}^{2} - 3) \\ =2(4 - 3) \\ = 2(1) \\ = 2 \: \: \: \: \: hence \: proved$