Question

arccos cos (2 arccot(2^1/2-1))=?

Answer 1

$arccot(\frac{2^1}{2}-1)=arccot(1-1)=arccot0=90^o,\;because\;cot90^o=0\\2arccot0=2\cdot90^o=180^o\\cos180^o=-1\\arccos(-1)=180^o\\arccos\ cos(2arccot(\frac{2^1}2-1)=180^o=\pi$
Note:
Range of principal usual value α for arccos is 0 ≤ α ≤ π and for arcot is 0 < α < π