Proving an Equation Involving k: A Homework Challenge

[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!