Given that $\displaystyle cotA=K$ and that $\displaystyle A$ is acute, express $\displaystyle sec2A$ in terms of $\displaystyle K$
Hello PunchHere are the formulae you'll need:If $\displaystyle A$ is acute, $\displaystyle \cot A = \frac{\text{adjacent}}{\text{opposite}}=\frac{K}{1 }$, so you can find $\displaystyle \cos A$ using Pythagoras' Theorem.Can you complete it now?
$\displaystyle \sec 2A = \frac{1}{\cos 2A}$
$\displaystyle \cos2A = 2 \cos^2A -1$
Grandad