Solving a Trigonometry Proof: 1+ cos Ө =?

[Alethia]

Yes it is me again. :D Now with a trig problem XD

I was doing some problems on my homework in math, Trigonometry and I had problems proving this proof:

1+ cos Ө = csc Ө + cot Ө

I've worked it out until I simplified the right side to:

sin Ө
-----
1+ cos Ө

And then I realized that was the half identity of tangent. I can;t make the connnection further to make the proof true. Please help! Have I simplified it wrong?

edit: the Ө is supposed to represent theta... but it keeps showing up like a square.. but you know what I mean. :D

 

[Parth Dave]

isnt csc = 1/sin and cot = cos/sin?

if that is so than the RS:
1/sin + cos/sin
(1+cos)/sin

(forgive me for not putting in thetas)

 

[Alethia]

Yeah that is what I got, but it's not eqaul to the left side, which is what I am supposed to do.

 

[Hurkyl]

Do you believe the identity is correct?

 

[Alethia]

See that's why I am confused. I've checked my work about a million times (maybe 5 or so times :D) and I keep coming up with the same solution. I checked the answer in the book and it says that the proof is true... so either I'm doing something wrong or it's an error in the book. :1

 

[Integral]

There must be a misprint, I did a quick calculation to show that they are equal at some point but certianly not in general
x.....1+cos(x)...csc(x)+cot(x)
0.1...1.995004165...19.98333055
0.2...1.980066578...9.966644423
0.3...1.955336489...6.616591506
0.4...1.921060994...4.933154876
0.5...1.877582562...3.916317365
0.6...1.825335615...3.232728144
0.7...1.764842187...2.739512159
0.8...1.696706709...2.36522242
0.9...1.621609968...2.070157361
1...1.540302306...1.830487722
1.1...1.453596121...1.631041424
1.2...1.362357754...1.461695947
1.3...1.267498829...1.315435692
1.4...1.169967143...1.187241832
1.5...1.070737202...1.073426149
1.6...0.970800478...0.971214601