Currently, the output for inputs involving sec or the other reciprocal trig functions seem to return expressions in terms of reciprocals, e.g.:
expand(integrate(6*sec(2*y)^7*tan(2*y)^3, y));
> 1/(3*cos(2*y)^9)\-3/(7*cos(2*y)^7)
Is there any way to have this returned in terms of sec(2*y) instead? I checked the documentation for display and the documentation for trigonometric functions but didn't see anything that seemed to address this.
Looks like trigreduce handles it (thanks to Stavros Macrakis for this info).
(%i2) 1/(3*cos(2*y)^9) - 3/(7*cos(2*y)^7);
1 3
(%o2) ----------- - -----------
9 7
3 cos (2 y) 7 cos (2 y)
(%i3) trigreduce(%);
9 7
sec (2 y) 3 sec (2 y)
(%o3) --------- - -----------
3 7