Question

Using the double angle of half angle formula, how do you simplify `(1-cos 4 theta)/(sin4theta)`?

Answer 1

Use the 2 trig identities:

`sin (2a) = 2. sin (a). cos (a)` and
`1 - cos (2a) = 2. sin^2 (a)`

`y = (1 - cos 4x)/sin (4x)` =
`= [2. sin^2 (2a)]/[2. sin (2a). cos (2a)]` = `tan (2a)`