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Question: The value of \(\lim_{|x| \rightarrow \infty}\)cos (tan–1 (sin (tan–1x))) is equal to –...

The value of lim⁡∣x∣→∞\lim_{|x| \rightarrow \infty}cos (tan–1 (sin (tan–1x))) is equal to –

A

–1

B

2\sqrt{2}

C

−12- \frac{1}{\sqrt{2}}

D

12\frac{1}{\sqrt{2}}

Answer

12\frac{1}{\sqrt{2}}

Explanation

Solution

cos (tan–1 sin (tan–1x)

cos (tan–1 sin sin–1 )

cos tan–1 (x1+x2)\left( \frac { x } { \sqrt { 1 + x ^ { 2 } } } \right)

cos cos–1

= = 12\frac { 1 } { \sqrt { 2 } }