Question

How do you determine graphically and analytically whether `y_1=sinxsecx` is equivalent to `y_2=tanx`?

Answer 1

See below.

Explanation:

Identitites

`color(red)bb(secx=1/cosx)`

`color(red)bb(tanx=sinx/cosx)`

`sinxsecx=sinx/cosx=tanx`

The graph of `bb(sinxsecx)` will be identical to the graph of `bbtanx`.
We have just proved that:

`sinxsecx-= tanx`