A) 1
B) 2
C) 1/3
D) 3/2
Correct Answer: B
Solution :
\[\underset{\theta \to 0}{\mathop{\lim }}\,\,[3-4\,{{\sin }^{2}}\theta ]-1=2.\] Aliter : \[\underset{\theta \to 0}{\mathop{\lim }}\,\,\frac{\sin 3\theta -\sin \theta }{\sin \theta }=\underset{\theta \to 0}{\mathop{\lim }}\,\,\frac{\sin 3\theta }{\sin \theta }-\underset{\theta \to 0}{\mathop{\lim }}\,\,\frac{\sin \theta }{\sin \theta }\] \[=\frac{3}{1}-1=2.\] You may also apply L-Hospital rule.
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