Question

Graph the expression sec2 x - sec2 x sin2 x on your calculator. Determine what constant or single function is equivalent to the given expression.

Answer 1

The given function is
f(x) = sec²x - sec²x sin²x

Note that
sin²x + cos²x = 1, so that 1 - sin²x = cos²x.
Also, sec(x) = 1/cos(x).

Therefore
f(x) = sec²x(1 - sin²x)
      = sec²x cos²x
      = 1

Answer:
The graph of the given function should be a constant value of 1.

The graph is shown below.