1. ## verifying identities...

good evening again to all..

how would i verify that..

[ 1 / cot x - csc x ] + [ 1 / cot x - csc x ] = 2 cot?????

thanks.. ^^

2. Originally Posted by riasantos
good evening again to all..

how would i verify that..

[ 1 / cot x - csc x ] + [ 1 / cot x - csc x ] = 2 cot?????

thanks.. ^^
You could start by either using brackets correctly or using LaTeX.

Is it

$\frac{1}{\cot{x} - \csc{x}} + \frac{1}{\cot{x} - \csc{x}}$

or

$\frac{1}{\cot{x}} - \csc{x} + \frac{1}{\cot{x}} - \csc{x}$?

3. it is the first one. ^^

4. $\frac{1}{\cot{x} - \csc{x}} + \frac{1}{\cot{x} - \csc{x}} = \frac{2}{\cot{x} - \csc{x}}$

$= \frac{2(\cot{x} + \csc{x})}{(\cot{x} - \csc{x})(\cot{x} + \csc{x})}$

$= \frac{2(\cot{x} + \csc{x})}{\cot^2{x} - \csc^2{x}}$

$= \frac{2(\cot{x} + \csc{x})}{-1}$

$= -2(\cot{x} + \csc{x})$

I don't know if you can go any futher...

5. Is not this identity?

$\frac{1}{\cot x - \csc x} + \frac{1}{\cot x + \csc x} = -2\cot x$

6. Originally Posted by danielomalmsteen
Is not this identity?

$\frac{1}{\cot x - \csc x} + \frac{1}{\cot x + \csc x} = -2\cot x$

That's not what the original question was...

But if it IS this...

$\frac{1}{\cot{x} - \csc{x}} + \frac{1}{\cot{x} + \csc{x}}$

$= \frac{\cot{x} + \csc{x}}{(\cot{x} - \csc{x})(\cot{x} + \csc{x})} + \frac{\cot{x} - \csc{x}}{(\cot{x} - \csc{x})(\cot{x} + \csc{x})}$

$= \frac{\cot{x} + \csc{x} + \cot{x} - \csc{x}}{(\cot{x} - \csc{x})(\cot{x} + \csc{x})}$

$= \frac{2\cot{x}}{\cot^2{x} - \csc^2{x}}$

$= \frac{2\cot{x}}{-1}$

$= -2\cot{x}$.