use trig identities to rewrite:

Question

(1/(1-cos4v))-(1/(1+cos4v))

Answer 1

Use a common denominator of (1-cos4v)(1+cos4v) = 1 - cos^2 4v = sin^2 4v

Then add up the numerator terms.

(1 + cos 4v -(1 - cos4v)/sin^2 4v

= 2 cos 4v/sin^2 4v