Proving 1/k = (1-sin x)/cos x given k = (1+sin x)/cos x

[icystrike]

Homework Statement

k=$$\frac{1+sinx}{cosx}$$
prove that $$\frac{1}{k}$$=$$\frac{1-sinx}{cosx}$$

thanks in advance

Homework Equations

The Attempt at a Solution

i tried substitution of 1 with
cos^2(x)+sin^2(x) and
cosec^2(x)-cot^2(x) and
sec^2(x)-tan^2(x)

but I am stucked agn..

 

[gabbagabbahey]

Start by inverting your expression for k to get: $$\frac{1}{k}=\frac{\cos x}{1+\sin x}$$ ...then multiply both your numerator and denominator by $(1- \sin x)$ and simplify...what do you get?

 

[icystrike]

oh..yah.. thanks loads. i will get the answer!