Involving sin^{-1}(((1-(1+c z^{2})^{1/2})/2)^{1/2})

Involving sin^{-1}(((1-(1+z^{2})^{1/2})/2)^{1/2}) and sec^{-1}(-i/z)

Involving sin^{-1}(((1-(1-z^{2})^{1/2})/2)^{1/2}) and sec^{-1}(1/z)