Chapter 14.3, Problem 28PPS

To determine

To Calculate:The value of $\text{cosec}\frac{5\pi }{12}$ .

Answer to Problem 28PPS

  $\frac{2\sqrt{2}}{\sqrt{3}+1}$

Explanation of Solution

Given information:

We know that, the given expression is $\text{cosec}\frac{5\pi }{12}$ .

Formula used:

  $\sin (\text{A}+\text{B})=\mathrm{s}\text{inΑcosΒ}+\text{cosΑsinΒ}.$

Calculation:

  $\begin{array}{l}\sin \frac{5\pi }{12}=\sin {75}^{\circ }\text{.}\\ =\sin ({45}^{\circ }+{30}^{\circ })\\ =\sin {45}^{\circ }\cos {30}^{\circ }+\cos {45}^{\circ }\sin {30}^{\circ }\\ =\frac{1}{\sqrt{2}}\cdot \frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\cdot \frac{1}{2}\\ =\frac{\sqrt{3}+1}{2\sqrt{2}}\\ \therefore \text{cosec}\frac{5\pi }{12}=\frac{2\sqrt{2}}{\sqrt{3}+1}\end{array}$