Question: Evaluate the following

1. \(\underset{\theta \to 0}{\mathop{\lim }}\,\frac{\tan \left( 3\theta \right)}{2\theta \cos \left( 5\theta \right)}=\underset{\theta \to 0}{\mathop{\lim }}\,\frac{\sin \left( 3\theta \right)}{2\theta \cos \left( 3\theta \right)\cos \left( 5\theta \right)}=\underset{\theta \to 0}{\mathop{\frac{3}{2}\lim }}\,\frac{\sin \left( 3\theta \right)}{3\theta \cos \left( 3\theta \right)\cos \left( 5\theta \right)}=\frac{3}{2}\)
2. \({{D}_{x}}\frac{\sin x\sec x}{1-{{\cos }^{2}}x}\) at \(x=\pi /6\)

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