Answer:
see explanation
Step-by-step explanation:
Using the Pythagorean identity
cos²A + sin²A = 1 ( divide terms by cos²A )
[tex]\frac{cos^2A}{cos^2A}[/tex] + [tex]\frac{sin^2A}{cos^2A}[/tex] = [tex]\frac{1}{cos^2A}[/tex] , that is
1 + tan²A = sec²A ← as required
