Not too sure if this question is right. Prove that:
$\displaystyle \dfrac{\cos{x}}{1-\tan{x}}+\dfrac{\sin{x}}{\cot{x}}=1$
To prove this identity take only the LHS and manipulate until you get the RHS.
$\displaystyle \dfrac{\cos{x}}{1-\tan{x}}+\dfrac{\sin{x}}{\cot{x}}$
First make a common denominator
$\displaystyle \dfrac{\cos{x}\cot{x}+\sin{x}(1-\tan{x})}{(1-\tan{x})\cot{x}}$
Now do some simplifying