Answer:
[tex]cos^{4}[/tex] x
Step-by-step explanation:
Using the trigonometric identities
1 + tan²x = sec²x and 1 - sin²x = cos²x
secx = [tex]\frac{1}{cosx}[/tex]
Given
[tex]\frac{1-sin^2x}{1+tan^2x}[/tex]
= [tex]\frac{cos^2x}{sec^2x}[/tex]
= [tex]\frac{cos^2x}{\frac{1}{cos^2x} }[/tex]
= cos²x × cos²x
= [tex]cos^{4}[/tex] x
