sec(x)+tan(x)=t
tan(x)=?(in form of t)
A quick rundown...As typical with me this is a rather "brute force" approach. I'll leave the details to the reader.
First put the equation into sines and cosines. Then solve for sin(x):
Hold on to this equation.
Now square both sides and use to put the equation in terms of only cosine. You can factor out a cos(x) from each side. Then solve for cos(x) getting:
Now put this expression for cos(x) into the above sin(x) equation. Then
Notice that this equation does not have the same domain as the original equation. I'll leave the details of that to you as well.
-Dan