Question

Folks,

I'm trying to evaluate (1/2)sin(2arcsec(-8)) where arcsec is the inverse secant. The answer is supposed to be 3sqrt(7)/128. I'll post a sketch of what I've done so far.

Answer 1

. I'm not sure how deal with the 2arcsec(-8)

Answer 2

\[arcsec(-8) = \frac{\pi}{2}+\arcsin(1/8)\]
If that sounds weird, draw a sketch and you might notice why.

Answer 3

It might be an equivalence, but how does that become 3sqrt(7)/128?

Answer 4

Is there an identity I'm missing?