$\operatorname{cosec}^{-1} \sqrt{14}+\cot ^{-1}\left(\frac{5}{2}\right)$ = ?

Question

Accepted Answer

গ. $	an ^{-1}(0.76)$

ব্যাখ্যা: ধরি, $A = \operatorname{cosec}^{-1}(\sqrt{14}) \implies \sin A = \frac{1}{\sqrt{14}}$।
সুতরাং, $	an A = \frac{1}{\sqrt{14 - 1}} = \frac{1}{\sqrt{13}}$।
আবার, $B = \cot^{-1}\left(\frac{5}{2}ight) \implies 	an B = \frac{2}{5}$।
এখন,
$	an(A + B) = \frac{	an A + 	an B}{1 - 	an A 	an B} = \frac{\frac{1}{\sqrt{13}} + \frac{2}{5}}{1 - \frac{1}{\sqrt{13}} \cdot \frac{2}{5}} = \frac{5 + 2\sqrt{13}}{5\sqrt{13} - 2} \approx \frac{5 + 7.2111}{18.0278 - 2} = \frac{12.2111}{16.0278} \approx 0.7618 \approx 0.76$
অতএব, $A + B = 	an^{-1}(0.76)$।

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