Question

Using the formula
$\sin (A-B)=\sin A\cos B-\cos A\sin B$
Find the value of $\sin {15}^o$

• A. $\sqrt{3}$
• B. $\sqrt{3}+1$
• C. $\frac{\sqrt{3}-1}{2\sqrt{2}}$
• D. $\frac{\sqrt{3}+1}{2\sqrt{2}}$

Answer 1

The correct option is C $\frac{\sqrt{3}-1}{2\sqrt{2}}$

WE have to find value of $\sin {15}^o$

$=\sin ({45}^o-{30}^o)$

$=\sin {45}^o\cos {30}^o-\cos {45}^{o}sin{30}^o$

$=\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}-\frac{1}{\sqrt{2}}\times \frac{1}{2}$

$=\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}-\frac{1}{\sqrt{2}}\times \frac{1}{2}$

$=\frac{\sqrt{3}-1}{2\sqrt{2}}$