lim(x→1/√2) (sin(cos^-1)x-x)/(1 - tan(cos^-1x)) is equal to:

Question

\(\lim\limits_{x \to {1/√2}}\frac{sin(cos^{-1}x)-x}{1-tan(cos^{-1}x)}\) is equal to:

lim(x→1/√2) (sin(cos^-1)x-x)/(1 - tan(cos^-1x))

(A) √2

(B) -√2

(C) 1/√2

(D) -1/√2

Answer 1

Correct option is (D) -1/√2

\(\lim\limits_{x \to {1/√2}}\frac{sin(cos^{-1}x)-x}{1-tan(cos^{-1}x)}\)