The value of the expression sin[cot^-1(cos(tan^-11))] is :

The correct answer is Option (1) → $\sqrt{\frac{2}{3}}$

$\sin(\cot^{-1}(\cos(\tan^{-1}1)))=\sin(\cot^{-1}\cos\frac{π}{4})$

$=\sin(\cot^{-1}\frac{1}{\sqrt{2}})$

Using pythagoras triangle

so $\sin(\cot^{-1}\frac{1}{\sqrt{2}})=\sqrt{\frac{2}{3}}$