Question

How do you verify `sec(x)-cos(x)=sin(x)tan(x)`?

Answer 1

This is trigonometric identity.
secx - cosx = sinxtanx
1/cosx-cosx = sinx.sinx/cosx
1-cos^2x/cosx=sin^2x/cosx
where: sin^2x = 1-cos^2x
therefore: sin^2x/cosx = sin^2/cosx

Explanation:

The identity of secx=1/cosx, tanx = sinx/cosx and 1-cos^2x = sin^2x