Question:
Using the formula, $\cos A=\sqrt{\frac{1+\cos 2 A}{2}}$, find the value of $\cos 30^{\circ}$, it being given that $\cos 60^{\circ}=\frac{1}{2} .$
Solution:
A = 30o
⇒ 2A = 2
By substituting the value of the given T-ratio, we get:
$\cos A=\sqrt{\frac{1+\cos 2 A}{2}}$
$\Rightarrow \cos 30^{\circ}=\sqrt{\frac{1+\cos 60^{\circ}}{2}}=\sqrt{\frac{1+\frac{1}{2}}{2}}=\sqrt{\frac{\frac{3}{2}}{2}}=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}$
$\therefore \cos 30^{\circ}=\frac{\sqrt{3}}{2}$