Chapter 13, Problem 27SGR

To determine

To find : The value of $\text{sin}\text{105°}$

Answer to Problem 27SGR

  $\sin 105°=\frac{\sqrt{3}+1}{2\sqrt{2}}$

Explanation of Solution

Given information :

We know that, the given information is $\text{sin}\text{105°}$ .

Formula Used :

  $\sin (A+B)=\sin A\cos B+\cos A\sin B$

Calculation :

The given equation is

  $\begin{array}{l}\sin 105°=\sin (180°-75°)\\ =\sin 75°\\ =\sin (45°+30°)\\ =\sin 45°\cos 30°+\cos 45°\sin 30°\\ =\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\times \frac{1}{2}\\ =\frac{\sqrt{3}}{2\sqrt{2}}+\frac{1}{2\sqrt{2}}=\frac{\sqrt{3}+1}{2\sqrt{2}}\end{array}$