Question

I can't figure out how to solve this: sec^2x-1/sec^2

I am very rusty on my fraction skills, can anyone recommend a video I can watch that explains how to solve fractions?

Answer 1

Answer: sin²θ

Step-by-step explanation:

First, convert sec into
`(1)/(cos)`, then use identity (cos²θ + sin²θ = 1) and simplify:

`(sec^(2)\theta - 1)/(sec^(2)\theta)`

=
`(sec^(2)\theta - 1)/(1)*(1)/(sec^(2)\theta)`

=
`((1)/(cos^(2)\theta) - 1)*((sec^(2)\theta)/(1))`

=
`((1)/(cos^(2)\theta) - (cos^(2)\theta)/(cos^(2)\theta))*((cos^(2)\theta)/(1))`

=
`((1 - cos^(2)\theta)/(cos^(2)\theta))*((cos^(2)\theta)/(1))`

=
`((sin^(2)\theta)/(cos^(2)\theta))*((cos^(2)\theta)/(1))`

=
`(sin^(2)\theta*cos^(2)\theta)/(cos^(2)\theta)`

= sin²θ