Question

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

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

Answer 1

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

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

$\therefore \cos {15}^o=\cos ({45}^o-{30}^o)=\cos {45}^o\cos {30}^o+\sin {45}^o\sin {30}^o$

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

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