Simplify sec(180°+x) using sum or difference identities.

Question

jamesj · Answer

Well cos(180 + x) = cos(180)cos(x) - sin(180)sin(x)
                            = -1        . cos(x) - 0 . sin(x)
                            = - cos(x)

Now, as sec x = 1 / cos x, it follows that

sec(180+x) = ....

anonymous · Answer

I got -sec(x), but my textbook says the answer is sec(x), because they for some reason started it off in a way that doesn't make sense to me: cos180*cosx-sin180*sinx -- makes sense except for that it's MINUS. It's plus?! Then also they plugged in a value of 1 for cos180... It's -1. So in the end the minus didn't matter anyway but I still don't know why they did that, and why they fluttered up the value of cos180, which is NEGATIVE, right? So I've got the same answer just negative... Who's right.

jamesj · Answer

You're right.  

This is error #4 from your book that I know about.  You need to buy a decent book and junk this one.

anonymous · Answer

You have no idea. Hahaha thank you though... My exam is in a week anyway so I might as well just keep on keepin on at this point