Verify identity - need to help a student work through this

[Guest]

(1-sec u)/(tan u) - (tan u)/(1 - sec u) = 2 cot u

[Guest]

[tex]\frac{1-\sec u}{\tan u} -\frac{\tan u}{1-\sec u}[/tex]

[tex]= \frac{(1-\sec u)^2 - \tan^2 u}{\tan u(1-\sec u)}[/tex]

[tex]= \frac{1-2\sec u+ \sec^2 u - \tan^2 u}{\tan u(1-\sec u)}[/tex]

[tex]= \frac{2-2\sec u}{\tan u(1-\sec u)}[/tex] (because [tex]\sec^2 u - \tan^2 u=1[/tex])

[tex]= \frac{2}{\tan u}[/tex]

[tex]= 2\cot u[/tex]

Hope that helped,

R. Baber.

[Guest]

Thank you!