Question

Which expression is equivalent to sec2x − 1?

Answer 1

tan²x

Explanation:

Using the Pythagorean identity

sin²x + cos²x = 1

Divide all terms by cos²x

`(sin^2x)/(cos^2x)` +
`(cos^2x)/(cos^2x)` =
`(1)/(cos^2x)`, that is

tan²x + 1 = sec²x ( subtract 1 from both sides )

tan²x = sec²x - 1