Question

HELP! prove tan5utan3u=(tan^2*4u-tan^2*u)/(1-tan^2*4u*tan^2u

Answer 1

you know tan(A+B) and tan(A-B) formula ??
write
5u = 4u+u
3u=4u-u
and use the formula.

Answer 2

\[\tan(A+B) = \frac{\tan A+\tan B}{1-\tan A.\tan B}\]
put, A=4u, B=u here.
\[\tan(A-B) = \frac{\tan A+\tan B}{1+\tan A.\tan B}\]
put, A =4u, B =u here also,
then just multiply both the equations, and you'll get your result.