# Math Help - Proving trig identity

1. ## Proving trig identity

Not too sure if this question is right. Prove that:

$\dfrac{\cos{x}}{1-\tan{x}}+\dfrac{\sin{x}}{\cot{x}}=1$

2. To prove this identity take only the LHS and manipulate until you get the RHS.

$\dfrac{\cos{x}}{1-\tan{x}}+\dfrac{\sin{x}}{\cot{x}}$

First make a common denominator

$\dfrac{\cos{x}\cot{x}+\sin{x}(1-\tan{x})}{(1-\tan{x})\cot{x}}$

Now do some simplifying

3. Originally Posted by pickslides
To prove this identity take only the LHS and manipulate until you get the RHS.

$\dfrac{\cos{x}}{1-\tan{x}}+\dfrac{\sin{x}}{\cot{x}}$

First make a common denominator

$\dfrac{\cos{x}\cot{x}+\sin{x}(1-\tan{x})}{(1-\tan{x})\cot{x}}$

Now do some simplifying
Yes, but the working doesn't work out

4. Substitute cot(x)=cos(x)/sin(x) and tan(x)=sin(x)/cos(x). Simplify. Now, you have your answer.