this one is giving me headache. I have tried maybe 7 tries and can not get close to what they want.

express the fallowing in terms of a single function.

$\displaystyle sec \theta - tan \theta $ in terms of $\displaystyle sin \theta $ .

I can only use the elementary identities. Pythagorean Reciprocal Co-function even/odd.

the answer to this in the book is $\displaystyle \frac{\sqrt{1-sin\theta}}{\sqrt{1+sin\theta}} $ which i can not get.

2 questions...

1) can I take the square root of the expression and multiply through the way you can with an equation? I know you can multiply by the conjugate of the denominator. but im not sure about the other two.

2) I can't find the right strategy. I was thinking get a single term in numerator and denominator that equal part of the Pythagorean that have been squared. and go from there. but that seems to be long way around.

any steps or ideas would be great.