MCQ
$\mathop {\lim }\limits_{\theta \to 0} \frac{{\sin 3\theta - \sin \theta }}{{\sin \theta }} = $
  • A
    $1$
  • $2$
  • C
    $1/3$
  • D
    $3/2$

Answer

Correct option: B.
$2$
b
(b) $\mathop {\lim }\limits_{\theta \to 0} \,[3 - 4\,{\sin ^2}\theta ] - 1 = 2.$

Aliter : $\mathop {\lim }\limits_{\theta \to 0} \,\frac{{\sin 3\theta - \sin \theta }}{{\sin \theta }} $

$= \mathop {\lim }\limits_{\theta \to 0} \,\frac{{\sin 3\theta }}{{\sin \theta }} - \mathop {\lim }\limits_{\theta \to 0} \,\frac{{\sin \theta }}{{\sin \theta }}$

$ = \frac{3}{1} - 1 = 2.$

You may also apply $L-$ Hospital rule.

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