arcexsec ⁡ ( y ) = arcsec ⁡ ( y + 1 ) = arccos ⁡ ( 1 y + 1 ) = arctan ⁡ ( y 2 + 2 y ) {\displaystyle \operatorname {arcexsec} (y)=\operatorname {arcsec}(y+1)=\arccos \left({\frac {1}{y+1}}\right)=\arctan({\sqrt {y^{2}+2y}})} [26][32][33] (for y ≤ −2 or y ≥ 0)[26]