Question

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

Answer 1

Put $A={30}^{\circ }$ then $2A={60}^{\circ }$

$\cos A=\sqrt{\frac{1+\cos 2A}{2}}$

$\cos {30}^{\circ }=\sqrt{\frac{1+\cos {60}^{\circ }}{2}}=\sqrt{\frac{1+\frac{1}{2}}{2}}=\sqrt{\frac{\frac{3}{2}}{2}}$

The value of $\cos {30}^{\circ }$ is $\frac{\sqrt{3}}{2}$.