# Trigonometric Identities

#### Tekker

Joined Apr 22, 2005
33
Hi all,

I've got a trig identity problem that neither my friend or I could figure out. It's also an even problem so I can't check the procedure in the book.

Rich (BB code):
 1 - cos x   sin x
--------- + --------- = 2 csc x
sin x   1 - cos x
The answer on the left is supposed to match the side on the right, but I got sin x for the left side. Our teacher doesn't want us multiplying things by both sides, so we have to simplify the part on the left and it should equal the part on the right.

If anyone can offer any help, I'd really appreciate it!

-tkr

#### hgmjr

Joined Jan 28, 2005
9,029
Originally posted by Tekker@Feb 27 2006, 08:35 PM
Hi all,

I've got a trig identity problem that neither my friend or I could figure out. It's also an even problem so I can't check the procedure in the book.

Rich (BB code):
 1 - cos x     sin x
--------- + --------- = 2 csc x
sin x     1 - cos x
The answer on the left is supposed to match the side on the right, but I got sin x for the left side. Our teacher doesn't want us multiplying things by both sides, so we have to simplify the part on the left and it should equal the part on the right.

If anyone can offer any help, I'd really appreciate it!

-tkr
[post=14424]Quoted post[/post]​
Rich (BB code):
(sin x * sin x) + (cos x * cos x) = 1
Using the above identity on the left side and converting the right side to

Rich (BB code):
   2
------
sin x
I was able to get the left side to equal the right side with this to identities

hgmjr

#### Tekker

Joined Apr 22, 2005
33
I've been trying to use the "(sin x * sin x) + (cos x * cos x) = 1" identity also, but it ain't coming together.

We just started learning these and unfortunately I don't have all the little tricks down yet that our book shows, so I'm sure I'm doing this the hard way. lol I started mine off by getting a common denominator and adding the two equations, then from there I just randomly plug away with that trig identity whenever I get something to match. But it goes on forever and it doesn't give me the right answer when I'm done.

Could you please break it down so I can see what you did?

Thanks,
-tkr

#### Polgi-Wan

Joined Sep 26, 2005
11
it's been ages so here's a try. . . .

(1-cosx)^2 + sin^2x
_________________
(sinx) (1-cosx)

1-2cosx + cos^2x + sin^2x
________________________
(sinx) (1-cosx)

2-2cosx
_____________
(sinx)(1-cosx)

2 (1 -cosx)
__________
sinx (1 - cosx)

2
----
sinx

= 2 cscx

hope this helps! hah, i graduated high school back in 1992 haha. . . .

#### Tekker

Joined Apr 22, 2005
33
D'oh! I see what I did wrong. For some reason I was thinking the middle terms would cancel for (1-cosx)^2, so I guess I was treating it like the difference of squares.... but backwards.... or something...... and I ended up with 1 - cos^2 x instead of 1 - 2 cos x + cos^2 x.

Geeesh! I was looking at the stuff after that trying to get my identities to cancel every thing and no wonder I could never get it to work since I messed up with the basic algebra. This has been a long term and it's only going to get worse before it gets better. :wacko:

Thanks for the help guys!

-tkr