Question

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

Answer 1

`cos^(4)` x

Explanation:

Using the trigonometric identities

1 + tan²x = sec²x and 1 - sin²x = cos²x

secx =
`(1)/(cosx)`

Given

`(1-sin^2x)/(1+tan^2x)`

=
`(cos^2x)/(sec^2x)`

=
`(cos^2x)/((1)/(cos^2x) )`

= cos²x × cos²x

=
`cos^(4)` x