Question

Use the fundamental identities to simplify the expression. Please, someone, help me? 1 − cos2 x / sec2 x − 1

Answer 1

= `cos^2 x`

Explanation:

`f(x) = (1- cos^2 x)/(sec^2 x - 1)`
Note that:
`1 - cos^2 x = sin^2 x`
`sec^2 x - 1 = 1/cos^2 x - 1 = (1 - cos^2 x)/(cos^2 x)`
`= sin^2 x/(cos^2 x)`
Hence,
`f(x) = (sin^2 x)/(sin^2 x/cos^2 x) = cos^2 x`