1. ## Pythagorean Identities

Prove that $secx + cosecxcotx \equiv secx cosec^2x$

I am having real trouble with these pythagorean identities, I have the rules but don't even know where to start.

2. Originally Posted by greghunter
Prove that $secx + cosecxcotx \equiv secx cosec^2x$

I am having real trouble with these pythagorean identities, I have the rules but don't even know where to start.
If you know the identities you will remember that $\cot^2{x} +1 = cosec^2{x}$.

If we put this into the right hand side we get $secx(\cot^2{x} +1)$.

$\frac{1}{\cos{x}}(\cot^2{x} +1)$

$\frac{\cos^2{x}}{\sin^2{x}\cos{x}} + \frac{1}{\cos{x}}$

Can you finish this off?

3. Oh just to note, it's perfectly legitimate to start on either side of the equation and make that equal to another.

4. Thanks Craig,
I think I just need to do some more practice on these

5. Originally Posted by greghunter
Thanks Craig,
I think I just need to do some more practice on these
No problem. As long as you remember $\sin^2{x} + \cos^2{x} = 1$ this is all you need, just divide through by either $\sin^2{x}$ or $\cos^2{x}$ to get the other two.

That's also providing you remember all the double angle formulas etc.