sec = 7/2 and is in Q1, then what is double angle of tan?

Answer 1

not quite sure what "double angle of tan" means, but if you want tan(u) where u is in QI and sec(u) = 7/2, then

draw the triangle. clearly tan(u) = √45/2 = 3√5/2. So,

tan(2u) = 2tan(u)/(1-tan^2(u))
= 2(3√5/2)/(1-45/4) = -12√5/41