Question

prove that (cos)2 theta =1/1+tan2 theta
please answe me

Answer 1

$right \: side = \frac{1}{1 + { \tan( \theta)}^{2} } \\ = \frac{1}{ { \sec( \theta) }^{2} } \\ = \frac{1}{ \sec( \theta) \times \sec( \theta) } \\ = \cos( \theta) \times \cos( \theta) \\ = {\cos( \theta)}^{2} \\ = left \: side\\ hence \: proved$