Question

Evaluate : cos(360+Q) cosec(360+Q) tan(90+Q)/sec(90+Q) cos(360-Q) cot(90+Q)

Answer 1

$$\begin{gathered} \frac{\cos \left(360+\mathrm{\theta }\right)\mathrm{cosec}\left(360+\mathrm{\theta }\right)\tan \left(90+\mathrm{\theta }\right)}{\sec \left(90+\mathrm{\theta }\right)\cos \left(360-\mathrm{\theta }\right)\cot \left(90+\mathrm{\theta }\right)} \\ =\frac{\cos \mathrm{\theta }.\mathrm{cosec}\mathrm{\theta }.\left(-\cot \mathrm{\theta }\right)}{\left(-\mathrm{cosec}\mathrm{\theta }\right).\cos \mathrm{\theta }.\left(-\tan \mathrm{\theta }\right)} \\ =-\frac{\cot \mathrm{\theta }}{\tan \mathrm{\theta }} \\ =-{\cot }^2\mathrm{\theta } \end{gathered}$$