Question

$cos ^{2} (1 + \tan ^{2} ) = 1$

Answer 1

Hello here is your answer by Sujeet yaduvanshi ☝☝

Answer 2

Hey there!

$\cos ^{2} x(1 + \tan ^{2} x) \\ \\ = ( \cos ^{2} x + \cos ^{2} x \tan ^{2} x) \\ \\ = ( \cos ^{2} x + \cos ^{2}x \times \frac{ {sin}^{2} x}{ {cos}^{2}x } ) \\ \\ = ( \cos ^{2} x + \cancel{\cos ^{2}x} \times \frac{ {sin}^{2} x}{ \cancel{ {cos}^{2}x } }) \\ \\ = {cos}^{2} x \: + {sin}^{2} x \\ \\ = 1$

Formulae :

cos²x + sin²x = 1

tanx = sinx / cosx

Hope helped!