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  4. cos-1[cos(2cot-1 (√2-1))] =

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Q. $cos^{-1}[cos(2cot^{-1} (\sqrt{2}-1))] =$

Inverse Trigonometric Functions

Solution:

$cos^{-1}\left(cos\left(2\,tan^{-1} \left(\sqrt{2}+1\right)\right)\right)$
$= cos^{-1}\left(cos\left(2.67 \frac{1^{\circ}}{2}\right)\right)$
$= cos^{-1}\left(cos\,135^{\circ}\right)=\frac{3\pi}{4}$