Step-by-step explanation:
[tex] \cos \theta(1 + { \tan}^{2} \theta) \\ = \cos \theta \times { \sec}^{2} \theta \\ = \cos \theta \times \frac{1}{{ \cos}^{2} \theta} \\ = \frac{1}{{ \cos} \theta} \\ = \sec \theta \\ \\ \red{ \boxed{ \bold{\therefore \: \cos \theta(1 + { \tan}^{2} \theta)= \sec \theta }}} \\ [/tex]
