Question

$\underset{\theta \to 0}{lim}\cot \theta -cosec\theta$

• A. $0$
• B. $2$
• C. $4$
• D. None of these

Answer 1

The correct option is A $0$

$\underset{\theta \to 0}{lim}(\cot \theta -\csc \theta )=\underset{\theta \to 0}{lim}(\frac{\cos \theta }{\sin \theta }-\frac{1}{\sin \theta })$

$=\underset{\theta \to 0}{lim}\frac{-2{\sin }^2\theta /2}{2\sin \frac{\theta }{2}\cos \frac{\theta }{2}}=\underset{\theta \to 0}{lim}-\tan \theta /2$

$=0$