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

Question

Evaluate:

\(\lim\limits_{x\to 1/\sqrt2}(\frac{sin(cos^-1x)-x}{1-tan(cos^-1x)})\)

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

(1) -1/√2

(2) 1/√2

(3) -1

(4) 1

Answer 1

 \(\lim\limits_{x\to 1/\sqrt2}(\frac{sin(cos^-1x)-x}{1-tan(cos^-1x)})\)