Proving Trigonometric Identites

[meeklobraca]

Homework Statement

tan x + 1/tan x - 1 = sec x + csc x/sec x - csc x

Homework Equations

The Attempt at a Solution

Ive tried working with the right side and have gotten as far as sin x/cosxsinx - cos x/cosxsinx

Im not sure if I am just out to lunch, or on the right track. Any help would be awesome!

Thanks!

 

[gabbagabbahey]

Your expression is ambiguous the way you have written it. (Use either brackets or LaTeX)

Do you mean $$\frac{\tan(x)+1}{\tan(x)-1}=\frac{\sec(x)+\csc(x)}{\sec(x)-\csc(x)}$$ ?

If so, try working with the LHS: Express everything in terms of sines and cosines and then divide both the numerator and denominator by $\sin(x)$

 

[meeklobraca]

im not getting it. should i turn the 1 into sines or cosines? Or even how do I know to do that?

 

[NoMoreExams]

No you should turn the tan into sin/cos and the find common denominators, cancel, etc. etc.

 

[meeklobraca]

Oh I did that too.

I had sin/cos + cos/cos all divided by sin/cos - cos/cos

 

[NoMoreExams]

Well a/c + b/c = (a+b)/c and also (a/b)/(c/d) = (ad)/(bc) I heard maybe you should use that.

 

[meeklobraca]

Well I heard that gives me sin x cos x + cos^2 x / sin x cos x - cos ^2 x

 

[NoMoreExams]

Umm why haven't you canceled the cos

 

[meeklobraca]

Your right, now I have sin x + cos x / sin x - cos x ?

 

[NoMoreExams]

Now compare that to what you are trying to get to...

 

[meeklobraca]

I got it. I went with the RHS side though, and converted it to the LHS. Thanks for your help!