Question

How do you prove `Sec(x) - cos(x) = sin(x) * tan(x)`?

Answer 1

I changed `sec` and `tan`:

Explanation:

We can change the `sec` and `tan` to write:
`1/cos(x)-cos(x)=sin(x)Sin(x)/cos(x)`

rearranging the left and right sides:

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

and remeber that: `sin^2(x)=1-cos^2(x)`

to write:

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