Question

(1-cos^2x)(1+tan^2x)=tan^2x

Answer 1

see explanation

Explanation:

Using the trigonometric identities

1 + tan²x = sec²x

1 - cos²x = sin²x and sec x =
`(1)/(cosx)`

Consider the left side

(1 - cos²x)(1 + tan²x)

= sin²x × sec²x

= sin²x ×
`(1)/(cos^2x)`

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

= tan²x