Question

Question #396f2

Answer 1

It isn't.

Explanation:

Let's find a derivative of
`y=cosx+sinx/cosx-sinx`

`dy/dx=cos'x-sin'x+(sin'xtimescosx-sinxtimescos'x)/cos^2x`

`dy/dx=-sinx-cos+(cosxtimescosx-sinxtimes(-sinx))/cos^2x`

Simplifying:

`dy/dx=-sinx-cos+1/cos^2x`

If we graph our derivative:

`y=sec^2(x+22/7)`:
graph{-sinx-cosx+(1/cosx)^2 [-5, 5, -2, 8]}

And compare it to `y=sec^2(x+22/7)`

graph{(sec(x+22/7))^2 [-5, 5, -2, 8]}

We clearly see they cannot be the same, so the argument is false.