Question

How do you prove `Cosx + sinx tanx = secx`?

Answer 1

Proof in explanation.

Explanation:

Proving `cosx + sinxtanx -= secx`

`RHS = cosx + sinxtanx`
`=cosx + sinx*sinx/cosx`
`=cosx+sin^2x/cosx`
`=cos^2x/cosx +sin^2x/cosx`
`=(sin^2x+cos^2x)/cosx` [Pythagorean identity: `sin^2x+cos^2x=1`]
`=1/cosx`
`=secx = LHS`