text: how do i figure out restrictions and state them using an algebraic or graphical approach? secx-sinx=cosx+tanx an algebraic approach is easiest.  first, write everything in terms of sin & cos.  this gives:  1/cosx - sinx = cosx + sinx/cosx.  always check square roots to make sure there are no negative numbers inside it (not applicable here) and another place is to look at denominators to make sure that they are not = 0.  you have a cosx term in the denominator, so set cosx = 0 and solve for x.  in this case, x = + or - (2n+1)pi/2 (or, the odd multiples of pi/2).  where the denominator = 0, the function has a vertical asymptote and that will be a restriction.  in other words, you can't use those values.  in this case, you can't use the odd multiples of pi/2.  anything else is okay.  restrictions occur where a function is not defined, such as under a sqrt where the quantity can't be negative, logx, where x cannot be 0 or negative, and places where the denominator = 0.  those are the places to look for restrictions.  let me know if this isn't clear.