The value of \cot^{-1} \left( \frac{\sqrt{1 + an^2(2)} - 1}{ an(2)} ight) - \cot^{-1} \left( \frac{\sqrt{1 + an^2\left(\frac{1}{2} ight)} + 1}{ an\left(\frac{1}{2} ight)} ight) is equal to

Question

The value of \cot^{-1} \left( \frac{\sqrt{1 + 	an^2(2)} - 1}{	an(2)} ight) - \cot^{-1} \left( \frac{\sqrt{1 + 	an^2\left(\frac{1}{2}ight)} + 1}{	an\left(\frac{1}{2}ight)} ight) is equal to

Accepted Answer

Answer: C. \pi - \frac{5}{4} \cot ^{-1}\left(\frac{|\sec 2|-1}{	an 2}ight)-\cot ^{-1}\left(\frac{\left|\sec \frac{1}{2}ight|+1}{	an \frac{1}{2}}ight) \begin{aligned} & =\cot ^{-1}\left(\frac{-1-\cos 2}{\sin 2}ight)-\cot ^{-1}\left(\frac{1+\cos \frac{1}{2}}{\sin \frac{1}{2}}ight) \ & =\pi-\cot ^{-1}(\cot 1)-\cot ^{-1}\left(\cot \frac{1}{4}ight) \ & =\pi-1-\frac{1}{4}=\pi-\frac{5}{4} \end{aligned}

The value of $ \cot^{-1} \left( \frac{\sqrt{1 + \tan^2(2)} - 1}{\tan(2)} \right) - \cot^{-1} \left( \frac{\sqrt{1 + \tan^2\left(\frac{1}{2}\right)} + 1}{\tan\left(\frac{1}{2}\right)} \right) $ is equal to

Answer

Explanation

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