If A=x→0limcos−1(cosx)sin−1(sinx) and B=x→0limx∣x∣ then (where [.] denotes greatest integer function)(A) A=1 (B) A does not exist (C) B = 0 (D) B=1

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Question

If $A = x \to 0 lim \frac{sin ^{- 1} ( sin x )}{cos ^{- 1} ( cos x )}$ and $B = x \to 0 lim \frac{∣ x ∣}{x}$ then (where [.] denotes greatest integer function)(A) A=1 (B) A does not exist (C) B = 0 (D) B=1

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William Discussed

A = x \to 0 lim \frac{sin ^{- 1} ( sin x )}{cos ^{- 1} ( cos x )}

and

B = x \to 0 lim \frac{∣ x ∣}{x}

then (where [.] denotes greatest integer function)(A) A=1 (B) A does not exist (C) B = 0 (D) B=1

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Question Text

A = x \to 0 lim \frac{sin ^{- 1} ( sin x )}{cos ^{- 1} ( cos x )}

and

B = x \to 0 lim \frac{∣ x ∣}{x}

then (where [.] denotes greatest integer function)(A) A=1 (B) A does not exist (C) B = 0 (D) B=1