Question

Using the formula, $\cos A=\sqrt{\frac{1+\cos 2A}{2}}$ , find the value of cos 30°, it being given that cos 60° = $\frac{1}{2}$.

Answer 1

A = 30^o
⇒ 2A = 2 $\times$ 30^o = 60^o

By substituting the value of the given T-ratio, we get:
$$\begin{gathered} \cos A=\sqrt{\frac{1+\cos 2A}{2}} \\ \Rightarrow \cos {30}^{\mathrm{o}}=\sqrt{\frac{1+\cos {60}^{\mathrm{o}}}{2}}=\sqrt{\frac{1+{\displaystyle \frac{1}{2}}}{2}}=\sqrt{\frac{{\displaystyle \frac{3}{2}}}{2}}=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2} \end{gathered}$$
∴ cos 30^o = $\frac{\sqrt{3}}{2}$