need help with Trig limit

[John45]

The limit as x approaches 0

5sec x - 1 / tan^2 x

I know tan^2 x = sec^2 x - 1

but i'm confused how to factor the denominate after and get the right answer

 

[tkhunny]

You could consider the difference of squares now in the denominator and create two with your best partial fraction skills.

Try:


\(\displaystyle \frac{3\cdot\sec(x)-1}{\sec(x)-1}-\frac{3\cdot\sec(x)}{\sec(x)+1}\)


Pretty clear what happens there.