# Thread: Proving Identity #2

1. ## Proving Identity #2

Prove
cot(theta)-tan(theta)=2cot(theta)

LS:

So far I have

cos(theta)/sin(theta)-sin(theta)/cos(theta)
=[cos^2(theta)-sin^2(theta)]/sin(theta)cos(theta)
=cos2(theta)/sin(theta)cos(theta)

I am stuck as to where to go now.
Can someone help me please?

2. Originally Posted by skeske1234
Prove
cot(theta)-tan(theta)=2cot(theta)
as posted, the above is not an identity.

perhaps you meant ...

$\cot{\theta} - \tan{\theta} = 2\cot(2\theta)$

???

3. Originally Posted by skeeter
as posted, the above is not an identity.

perhaps you meant ...

$\cot{\theta} - \tan{\theta} = 2\cot(2\theta)$

???

no no, the question says:
cot(theta)-tan(theta)=2cot(theta)

Ok, so if it is not an identity, how do I prove or know that it is not one?

4. Originally Posted by skeske1234
no no, the question says:
cot(theta)-tan(theta)=2cot(theta)

Ok, so if it is not an identity, how do I prove or know that it is not one?
show the equation is false for at least one value of $\theta$ ... try $\theta = \frac{\pi}{4}$, see what happens.

5. Originally Posted by skeske1234
no no, the question says:
cot(theta)-tan(theta)=2cot(theta)

Ok, so if it is not an identity, how do I prove or know that it is not one?
yeah skeske1234 is correct
If so