Question #396f2

1 Answer
Feb 6, 2018

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.