Question

Simplify: (1-sin^2 x)/(1+tan^2 x)

Answer 1

Answer:

$cos^{4}$ x

Step-by-step explanation:

Using the trigonometric identities

1 + tan²x = sec²x and 1 - sin²x = cos²x

secx = $\frac{1}{cosx}$

Given

$\frac{1-sin^2x}{1+tan^2x}$

= $\frac{cos^2x}{sec^2x}$

= $\frac{cos^2x}{\frac{1}{cos^2x} }$

= cos²x × cos²x

= $cos^{4}$ x