[squallie]

Okay, I'm having great difficulty in this one problem that I just can't seem to solve. I've attempted it, but in all honesty, I was just lost after simplifying the problem. Please, I really really need help on this for it determines whether I'm exempt or not for my midterms. I'm gonna rely on you guys to save me.

Solve tanx-sinx = secx - 1 for all values of x.
.........tanx+sinx...secx + 1

This problem may require identities and referring to the sin and cos graph.
Thank you everyone for your time. (Excuse the white dots. I was trying to align the problem. lOl.)

[Voltage]

it appears that any value for x works.

you can simplify left hand side to:
sinx/cosx -sinx 1/cosx - 1
----------------- = ---------------
sinx/cosx+sinx 1/cosx + 1

sinx(1/cosx -1) 1/cosx -1
----------------- = ----------
sinx(1/cosx+1) 1/cosx +1

cancel left hand side and they are identical so all values should work...please verify hah

[THEmerryJANE]

I got all values of x too.

It works when you cross multiply also.

(tanx - sinx)(secx + 1) = (tanx + sinx)(secx - 1)
tanxsecx + tanx - sinxsecx - sinx = tanxsecx - tanx + sinxsecx - sinx
tanx = sinxsecx
tanx = tanx
x = x

But I'm kind of skeptical because your problem says it might requires identities and refers to the sinx/cosx graph, which I have no idea what that might mean.

[squallie]

Ahh, thank you for your help, both of you. I actually found out that both of you are partially correct, and that the answer was "All real numbers except 90, 180, and 270." I also tackled the problem the way the both of you did, but in the end, I was still incorrect. And it did require looking at the cos curve in order to get the answers. Once again, thank you! It was a very difficult problem.