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

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

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- Jul 1st 2010, 08:43 PMacevipaProving trig identity
Not too sure if this question is right. Prove that:

$\displaystyle \dfrac{\cos{x}}{1-\tan{x}}+\dfrac{\sin{x}}{\cot{x}}=1$ - Jul 1st 2010, 08:53 PMpickslides
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 - Jul 1st 2010, 09:39 PMacevipa
- Jul 2nd 2010, 01:23 AMp0oint
Substitute cot(x)=cos(x)/sin(x) and tan(x)=sin(x)/cos(x). Simplify. Now, you have your answer.