Am I wrong or is the book wrong??? (Circular Functions)

[gta007]

Hi guys and gals.

Just dropping by to get a second opinion.

"If x = secø - tanø, prove that x + 1/x = 2secø and also find a simple expression for x - 1/x in terms of ø."

I've tried this a question a few times, with different substitutions such as 1/sinø for secø and sinø/cosø for tanø as well as multiplying by (secø - tanø)/(secø - tanø),
however, I always end with 2(1+sinø) / cosø. Am I missing something here, as I don't think that 1+sinø = 1, because 2secø = 2/cosø

Any help would be much appreciated. 

[gta007]

Don't worry, I worked it out. I kept thinking (1-sinø)^2 was 1-sin^2ø instead of 1 - 2sinø + sin^2ø