A) 0
B) - 1
C) 1
D) \[\infty \]
Correct Answer: C
Solution :
We have, \[\underset{\theta \to \frac{\pi }{2}}{\mathop{\lim }}\,\,\frac{\pi /2-\theta }{\cot \theta }\left( \frac{0}{0}form \right)\] Using L-Hospital rule, we get \[=\underset{\theta \to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{-1}{-\cos e{{c}^{2}}\theta }\] \[=\underset{\theta \to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{-1}{-1/{{\sin }^{2}}\theta }\] \[=\underset{\theta \to \frac{\pi }{2}}{\mathop{\lim }}\,{{\sin }^{2}}\theta =1\]
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