यदि x = log_e left( cot left( frac{pi}{4} + t | vedclass

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(B) दिया गया है $x = \log_e \left( \cot \left( \frac{\pi}{4} + 	heta ight) ight)$.हम जानते हैं कि $\sinh x = -	an(2	heta)$ और $\cosh x = \sec(2

Vedclass · Accepted Answer

$-\frac{1}{2}$

Vedclass · Answer

(B) दिया गया है $x = \log_e \left( \cot \left( \frac{\pi}{4} + 	heta ight) ight)$.हम जानते हैं कि $\sinh x = -	an(2	heta)$ और $\cosh x = \sec(2	heta)$.अतः $(\sinh x)(\cosh x) = -	an(2	heta) \sec(2	heta) = -\frac{\sin(2	heta)}{\cos^2(2	heta)}$.अब,सीमा $\lim_{	heta ightarrow 0} \frac{	heta}{-\sin(2	heta)/\cos^2(2	heta)} = \lim_{	heta ightarrow 0} -\frac{	heta}{\sin(2	heta)} \cdot \cos^2(2	heta) = -\frac{1}{2} \cdot 1 = -\frac{1}{2}$.

यदि $x = \log_e \left( \cot \left( \frac{\pi}{4} + \theta \right) \right)$ है,तो $\lim_{\theta \rightarrow 0} \frac{\theta}{(\sinh x)(\cosh x)} = $

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