I'll just do the first one:

tan(t) +  = sec(t)

Rationalize the denominator of the second term by
multiplying it by 

tan(t) + 

tan(t) + 

tan(t) + 

You know the identity .  When it
is solved like this  the right side
is the same form as the denominator and so we can write 
as 

tan(t) + 

And we cancel the cos(t) on top into the cos²(t) in the bottom

tan(t) +   

tan(t) + 

Now we substitute  for :



Combine the fractions (they already have a common denominator):









Edwin