posted by Natash .
simplify and write the trigonometric equation in terms of sine and cosine.
You have not provided an equation.
Equations have an "=" sign.
You must have left something out.
Perhaps they just want you to write the term tan^2x-sec^2x in terms of sines and cosines. If so, they should have said so.
from the main Pythagorean Identity we know
tan^2 x + 1 = sec^2 x
so tan^2x-sec^2x = tan^2 x - (tan^2 x + 1)