# Tigonometric Identies problem help!

1. Oct 30, 2004

### andyc18

I need hep verifying two trig identity problems

1. (cot-csc)^2 = (1-cos)/(1+cos)

2. sin2tan2/tan2-sin2 = 1

Any help?

2. Oct 30, 2004

### Dr Transport

The easiest way to prove trig identities is to express all of the quantites in terms of sines and cosines, then start rearranging from there......

3. Oct 30, 2004

### andyc18

I have tried doing that many times ..still having no luck..

4. Oct 31, 2004

### James R

Could you please write out your questions again, with the variables, and all bracketing correct?

There's no way to tell is, by sin2 you mean (sin x)<sup>2</sup> or sin 2x.

Also, in your second problem, do you mean

$$\frac{\sin^2 x \tan^2 x}{\tan^2 x} - \sin^2 x$$

or something else?

Notation is important.

5. Oct 31, 2004

### James R

Here's a solution to the first problem:

$$(\cot x - \mbox{cosec} x)^2\\ = \left(\frac{\cos x}{\sin x} - \frac{1}{\sin x}\right)^2\\ = \frac{(\cos x - 1)(\cos x - 1)}{\sin^2 x}\\ = \frac{(\cos x - 1)(\cos x - 1)}{1 - \cos^2 x}\\ = \frac{(\cos x - 1)(\cos x - 1)}{(1 + \cos x)(1 - \cos x)}\\ = \frac{1 - \cos x}{1 + \cos x}$$

Last edited: Oct 31, 2004