Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
1 + tan²x = sec²x
1 - cos²x = sin²x and sec x = [tex]\frac{1}{cosx}[/tex]
Consider the left side
(1 - cos²x)(1 + tan²x)
= sin²x × sec²x
= sin²x × [tex]\frac{1}{cos^2x}[/tex]
= [tex]\frac{sin^2x}{cos^2x}[/tex]
= tan²x
