જો alpha beta gamma 0 હોય,તો પદાવલિ cot | vedclass

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Question

(D) ધારો કે આપેલ પદાવલિ $S = \cot ^{-1}\left\{\beta+\frac{1+\beta^2}{\alpha-\beta}\right\}+\cot ^{-1}\left\{\gamma+\frac{1+\gamma^2}{\beta-\gamma}\rig

Vedclass · Accepted Answer

$\pi$

Vedclass · Answer

(D) ધારો કે આપેલ પદાવલિ $S = \cot ^{-1}\left\{\beta+\frac{1+\beta^2}{\alpha-\beta}ight\}+\cot ^{-1}\left\{\gamma+\frac{1+\gamma^2}{\beta-\gamma}ight\}+\cot ^{-1}\left\{\alpha+\frac{1+\alpha^2}{\gamma-\alpha}ight\}$ છે.$\cot^{-1}(x) = 	an^{-1}(1/x)$ નો ઉપયોગ કરતા:$S = 	an^{-1}\left(\frac{\alpha-\beta}{1+\alpha\beta}ight) + 	an^{-1}\left(\frac{\beta-\gamma}{1+\beta\gamma}ight) + 	an^{-1}\left(\frac{\gamma-\alpha}{1+\gamma\alpha}ight)$.$	an^{-1}(x) - 	an^{-1}(y) = 	an^{-1}\left(\frac{x-y}{1+xy}ight)$ સૂત્ર મુજબ:$S = (	an^{-1}\alpha - 	an^{-1}\beta) + (	an^{-1}\beta - 	an^{-1}\gamma) + (	an^{-1}\gamma - 	an^{-1}\alpha + \pi) = \pi$.

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