# Math Help - Identities

1. ## Identities

$tan(x-\frac{\pi}{2})= - cot x$

$\frac{tanx-tan\frac{\pi}{2}}{1+tanx+tan\frac{\pi}{2}}= -cotx$

$\frac{1}{1+0}$

I cant solve this identity can someone help me?

2. Hello, purplec16!

You can't use that compound-angle formula
. . because $\tan\tfrac{\pi}{2}$ is undefined.

$\tan\left(x-\tfrac{\pi}{2}\right) \:=\: -\cot x$

$\tan\left(x-\tfrac{\pi}{2}\right) \;=\;\frac{\sin(x-\frac{\pi}{2})}{\cos(x-\frac{\pi}{2})} \;=\;\frac{\sin x\cos\frac{\pi}{2} - \cos x\sin\frac{\pi}{2}}{\cos x\cos\frac{\pi}{2} + \sin x\sin\frac{\pi}{2}}$ . $=\; \frac{\sin x\cdot 0 - \cos x\cdot 1}{\cos x\cdot 0 + \sin x\cdot 1} \;=\;-\frac{\cos x}{\sin x} \;=\;-\cot x$

3. You are entirely overlooking the fact that $\tan\left(\frac{\pi}{2}\right)$ doesn't exist. You'll have to find some other way to proceed.

$\tan{\alpha} = \frac{\sin(\alpha)}{\cos(\alpha)}$

That might help.

4. Originally Posted by TKHunny
You are entirely overlooking the fact that $\tan\left(\frac{\pi}{2}\right)$ doesn't exist. You'll have to find some other way to proceed.

$\tan{\alpha} = \frac{\sin(\alpha)}{\cos(\alpha)}$

That might help.
Are you implying that what he did was wrong?

5. Originally Posted by purplec16
Are you implying that what he did was wrong?
Are you not able to see the fact that both are giving the similar hint?

6. Originally Posted by sa-ri-ga-ma
Are you not able to see the fact that both are giving the similar hint?
I really dont understand what you are sayin

7. Originally Posted by purplec16
Are you implying that what he [Soroban] did was wrong?
TKH is NOT implying that at all!!

Originally Posted by purplec16
I really dont understand what you are sayin
For goddness sake, please read and try to process the help that people are taking the time to give you.

Look at the timestamps on the replies by Soroban and TKH .... Soroban has actually given you the solution. And while he was giving it to you, TKH was typing a hint for you to think about.

The only thing that defies understanding here is why you are confused.

8. Originally Posted by mr fantastic
TKH is NOT implying that at all!!

For goddness sake, please read and try to process the help that people are taking the time to give you.

Look at the timestamps on the replies by Soroban and TKH .... Soroban has actually given you the solution. And while he was giving it to you, TKH was typing a hint for you to think about.

The only thing that defies understanding here is why you are confused.
Ok, thanks I guess..:S my mistake...