The value of 2 cot ^{-1} frac{1}{2} - cot ^{- | vedclass

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Question

(D) Given expression: $2 \cot ^{-1} \frac{1}{2} - \cot ^{-1} \frac{4}{3}$ Using the property $\cot ^{-1} x = 	an ^{-1} \frac{1}{x}$ for $x > 0$: $= 2

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$\frac{\pi}{2}$

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(D) Given expression: $2 \cot ^{-1} \frac{1}{2} - \cot ^{-1} \frac{4}{3}$ Using the property $\cot ^{-1} x = 	an ^{-1} \frac{1}{x}$ for $x > 0$: $= 2 	an ^{-1} 2 - 	an ^{-1} \frac{3}{4}$ Using the formula $2 	an ^{-1} x = \pi + 	an ^{-1} \frac{2x}{1-x^2}$ for $x > 1$: $= \pi + 	an ^{-1} \frac{2(2)}{1-2^2} - 	an ^{-1} \frac{3}{4}$ $= \pi + 	an ^{-1} \frac{4}{-3} - 	an ^{-1} \frac{3}{4}$ $= \pi - 	an ^{-1} \frac{4}{3} - 	an ^{-1} \frac{3}{4}$ $= \pi - (	an ^{-1} \frac{4}{3} + 	an ^{-1} \frac{3}{4})$ Using the property $	an ^{-1} x + 	an ^{-1} \frac{1}{x} = \frac{\pi}{2}$ for $x > 0$: $= \pi - \frac{\pi}{2} = \frac{\pi}{2}$

The value of $2 \cot ^{-1} \frac{1}{2} - \cot ^{-1} \frac{4}{3}$ is

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