# Proving trig identity

• July 1st 2010, 08:43 PM
acevipa
Proving trig identity
Not too sure if this question is right. Prove that:

$\dfrac{\cos{x}}{1-\tan{x}}+\dfrac{\sin{x}}{\cot{x}}=1$
• July 1st 2010, 08:53 PM
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
• July 1st 2010, 09:39 PM
acevipa
Quote:

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
• July 2nd 2010, 01:23 AM
p0oint
Substitute cot(x)=cos(x)/sin(x) and tan(x)=sin(x)/cos(x). Simplify. Now, you have your answer.