# Verify identity - need to help a student work through this

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

### Verify identity - need to help a student work through this

(1-sec u)/(tan u) - (tan u)/(1 - sec u) = 2 cot u
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### Re: Verify identity - need to help a student work through th

$$\frac{1-\sec u}{\tan u} -\frac{\tan u}{1-\sec u}$$

$$= \frac{(1-\sec u)^2 - \tan^2 u}{\tan u(1-\sec u)}$$

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

$$= \frac{2-2\sec u}{\tan u(1-\sec u)}$$ (because $$\sec^2 u - \tan^2 u=1$$)

$$= \frac{2}{\tan u}$$

$$= 2\cot u$$

Hope that helped,

R. Baber.
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### Re: Verify identity - need to help a student work through th

Thank you!
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