Help proving an identity

**masterkale** · April 22nd 2010, 11:28 AM

I have the identity (tanx/(1-cotx)) + (cotx/(1-tanx)) = 1 + tanx + cotx

I have started by turning everything into tan, but from there i can't figure it out. Any help would be much appreciated, thank you.

**Rapha** · April 22nd 2010, 11:57 AM

Hi and welcome to the forums

Originally Posted by masterkale

I have the identity (tanx/(1-cotx)) + (cotx/(1-tanx)) = 1 + tanx + cotx

I have started by turning everything into tan, but from there i can't figure it out. Any help would be much appreciated, thank you.

I think this is pretty basic, so

(by the way I'm going to use that $tan(x) = \frac{1}{cot(x)}$ )

$\frac{tan}{1-cot} + \frac{cot}{1-tan}$

$\frac{tan^2}{tan-1} + \frac{cot}{1-tan}$

$-\frac{tan^2}{1-tan} + \frac{cot}{1-tan}$

$\frac{cot - tan^2}{1-tan}$

$\frac{1 - tan^3}{tan(1-tan)}$

$\frac{(1 - tan)( 1 + tan +tan^2)}{tan(1-tan)}$

$\frac{( 1 + tan +tan^2)}{tan}$

$1 + tan + cot$

do you still have questions on that problem? Then let us know

Rapha

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