The value of is equal to (note: denotes the greatest integer less than or equal to ).

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

The value of lim⁡x→0(sin⁡−1[cos⁡x]+cos⁡−1[sin⁡x]−2sec⁡−1[sec⁡x])\lim_{x\to0}\left(\sin^{-1}[\cos x]+\cos^{-1}[\sin x]-2\sec^{-1}[\sec x]\right) is equal to (note: [k][k] denotes the greatest integer less than or equal to kk). (a) π2−2\frac{\pi}{2}-2 (b) π2\frac{\pi}{2} (c) π\pi (d) Non-existent

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