Chapter 14.4, Problem 18PPS

To determine

To Find:The value of $\sin {75}^{\circ }$

Answer to Problem 18PPS

  $\frac{1+\sqrt{3}}{2\sqrt{2}}$

Explanation of Solution

Given:

We know that the given Angle is $\sin {75}^{\circ }$

Calculation:

  $\begin{array}{l}\Rightarrow \sin {75}^{\circ }\\ \Rightarrow \sin ({30}^{\circ }+{45}^{\circ })\\ \because \sin (A+B)=\sin A\cos B+\cos A\sin B\\ \Rightarrow \sin ({30}^{\circ }+{45}^{\circ })=\sin {30}^{\circ }\cos {45}^{\circ }+\cos {30}^{\circ }\sin {45}^{\circ }\\ \Rightarrow \frac{1}{2}\times \frac{1}{\sqrt{2}}+\frac{\sqrt{3}}{2}\times \frac{1}{\sqrt{2}}\\ \Rightarrow \frac{1}{2\sqrt{2}}+\frac{\sqrt{3}}{2\sqrt{2}}\\ \Rightarrow \frac{1+\sqrt{3}}{2\sqrt{2}}\end{array}$