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.