You are given that

\(y=\frac1{\cos2x}.\)

(a) Show that

\(\frac{dy}{dx}=\frac{k\sin2x}{\cos^22x},\)

where \(k\) is a constant to be found.

(b) Find the values of \(x\) such that

\(\frac{dy}{dx}=\frac5{\sin2x}\)

for \(0\lt x\lt \frac{\pi}{2}\).