1. ## proving identities

how would i prove that csc x / cot x + tan X = cos???
it has been disturbing me for almost 3 days,, ..

hope you guys can help me...

thanks..

2. Originally Posted by riasantos
how would i prove that csc x / cot x + tan X = cos???
it has been disturbing me for almost 3 days,, ..

hope you guys can help me...

thanks..
We shouldn't have to waste time figuring out if you mean csc x / (cot x + tan X) = cos or (csc x / cot x) + tan X = cos. Use brackets to remove the ambiguity!

3. ## provind trigonometric identities..

umm.. okay.. thanks for the reply..

then the equation must be...

[csc (x) / cot (X) ] + tan (x) = cos (x)

how would i prove it???
thanks.. ^^

4. Originally Posted by riasantos
umm.. okay.. thanks for the reply..

then the equation must be...

[csc (x) / cot (X) ] + tan (x) = cos (x)

how would i prove it???
thanks.. ^^
Are you sure you wrote the identity correctly?

5. umm.. yes. why?? is it wrong???

6. Originally Posted by riasantos
umm.. yes. why?? is it wrong???
Yeah, that's not an identity. Counterexample: $\frac{\pi}{4}$

$sin\left(\frac{\pi}{4}\right) = cos\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt2}$

$tan\left(\frac{\pi}{4}\right) = cot\left(\frac{\pi}{4}\right) = 1$

Spoiler:
$\left[\frac{1}{sin\left(\frac{\pi}{4}\right)} \div cot\left(\frac{\pi}{4}\right)\right] + tan\left(\frac{\pi}{4}\right) = \sqrt{2} \div 1 + 1 = \sqrt{2}+1 \neq \frac{1}{\sqrt2}
$

7. thanks.. ^^

8. Originally Posted by riasantos
thanks.. ^^
However:

$\frac{csc(x)}{cot(x)+tan(x)} = cos(x)$ is an identity