Question

prove tan5utan3u=(tan^24utan^2u)/(1-tan^24utan^2u)

Answer 1

$\tan5u\tan3u=\dfrac{\tan^24u\tan^2u}{1-\tan^24u\tan^2u}$

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

$\dfrac{\tan^2\pi\tan^2\frac\pi4}{1-\tan^2\pi\tan^2\frac\pi4}=\dfrac{0(1)}{1-0(1)}=0$