$\begin{align}  & \text{Note:}\tfrac{\pi }{2}radian={{90}^{\circ }},\text{ }2\pi radian={{360}^{\circ }} \\ & \operatorname{cosec}({{90}^{\circ }}+\theta )=\frac{1}{\sin ({{90}^{\circ }}+\theta )} \\ & \operatorname{cosec}({{90}^{\circ }}+\theta )=\frac{1}{\sin {{90}^{\circ }}{{\cos }^{\circ }}+\cos {{90}^{\circ }}\sin \theta } \\ & \operatorname{cosec}({{90}^{\circ }}+\theta )=\frac{1}{\cos \theta +0}=\frac{1}{\cos \theta }=\frac{1}{a} \\ & \text{Also,} \\ & \sin \left( \tfrac{3\pi }{2}-\theta  \right)=\sin \tfrac{3\pi }{2}\cos \theta -\cos \tfrac{3\pi }{2}\sin \theta  \\ & \text{Note: }\tfrac{3\pi }{2}radian=\tfrac{3\pi }{2}\times \tfrac{{{180}^{\circ }}}{\pi }={{270}^{\circ }} \\ & \sin \left( \tfrac{3\pi }{2}-\theta  \right)=\sin {{270}^{\circ }}\cos \theta -\cos {{270}^{\circ }}\sin \theta  \\ & \sin \left( \tfrac{3\pi }{2}-\theta  \right)=(-1)\cos \theta -0\sin \theta =-\cos \theta =-a \\\end{align}$