Question

How do you verify `-(1/2)sec²(x) = -2sin²(x)csc²(2x)`?

Answer 1

`sin 2A = 2sin Acos A`

`-2sin^2 x csc^2 2x = -(2sin^2 x)/(sin^2 2x) = -(2sin^2 x)/(4sin^2 xcos^2 x) = -1/2sec^2 x`