Prove that $\displaystyle 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 $\displaystyle \cot^2{x} +1 = cosec^2{x}$.
If we put this into the right hand side we get $\displaystyle secx(\cot^2{x} +1)$.
$\displaystyle \frac{1}{\cos{x}}(\cot^2{x} +1)$
$\displaystyle \frac{\cos^2{x}}{\sin^2{x}\cos{x}} + \frac{1}{\cos{x}}$
Can you finish this off?
No problem. As long as you remember $\displaystyle \sin^2{x} + \cos^2{x} = 1$ this is all you need, just divide through by either $\displaystyle \sin^2{x}$ or $\displaystyle \cos^2{x}$ to get the other two.
That's also providing you remember all the double angle formulas etc.