mathop {lim }limits_{a to 0} frac{{sin a - ta | vedclass

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Question

(A) આપેલ લક્ષ: $\mathop {\lim }\limits_{a 	o 0} \frac{{\sin a - 	an a}}{{{{\sin }^3}a}}$$	an a$ ને $\frac{\sin a}{\cos a}$ તરીકે લખતા:$\mathop {\li

Vedclass · Accepted Answer

$ - \frac{1}{2}$

Vedclass · Answer

(A) આપેલ લક્ષ: $\mathop {\lim }\limits_{a 	o 0} \frac{{\sin a - 	an a}}{{{{\sin }^3}a}}$$	an a$ ને $\frac{\sin a}{\cos a}$ તરીકે લખતા:$\mathop {\lim }\limits_{a 	o 0} \frac{{\sin a - \frac{\sin a}{\cos a}}}{{{{\sin }^3}a}} = \mathop {\lim }\limits_{a 	o 0} \frac{{\sin a(\cos a - 1)}}{{\cos a \cdot \sin^3 a}}$$\sin a$ ને છેદતા:$= \mathop {\lim }\limits_{a 	o 0} \frac{{\cos a - 1}}{{\cos a \cdot \sin^2 a}}$$\sin^2 a = 1 - \cos^2 a = (1 - \cos a)(1 + \cos a)$ નિત્યસમનો ઉપયોગ કરતા:$= \mathop {\lim }\limits_{a 	o 0} \frac{{-(\cos a - 1)}}{{\cos a \cdot (1 - \cos a)(1 + \cos a)}}$$(1 - \cos a)$ ને છેદતા:$= \mathop {\lim }\limits_{a 	o 0} \frac{{-1}}{{\cos a(1 + \cos a)}}$$a = 0$ મૂકતા:$= \frac{{-1}}{{1(1 + 1)}} = -\frac{1}{2}$

$\mathop {\lim }\limits_{a \to 0} \frac{{\sin a - \tan a}}{{{{\sin }^3}a}}$ ની કિંમત શું થશે?

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