\(\tan5u\tan3u=\dfrac{\tan^24u\tan^2u}{1-\tan^24u\tan^2u}\)
This is not true (assuming I've understood the question correctly).
Consider \(u=\dfrac\pi4\). Then
\(\tan\dfrac{5\pi}4\tan\dfrac{3\pi}4=1(-1)=-1\)
while
\(\dfrac{\tan^2\pi\tan^2\frac\pi4}{1-\tan^2\pi\tan^2\frac\pi4}=\dfrac{0(1)}{1-0(1)}=0\)
