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Lim (1 - sin x)/(x - π/2)
= Lim (1 - sin x)/(x - π/2) . (1 + sin x)/(1 + sin x)
= Lim (1 - sin^2 x) / (x - π/2)(1 + sin x)
= Lim (cos^2 x) / -1(π/2 - x)(1 + sin x)
= Lim (cos x . cos x) / -1(π/2 - x)(1 + sin x)
= Lim (sin (π/2 - x) cos x) / -1(π/2 - x)(1 + sin x)
= Lim (sin (π/2 - x))/(-1(π/2 - x)) . (cos x)/(1 + sin x)
= -1 . (cos π/2)/(1 + sin π/2)
= -1 (0) / (1 + 1)
= 0