Using the formula, cos A


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



A = 30o
⇒ 2A = 2 ×">×× 30o = 60o

By substituting the value of the given T-ratio, we get:

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

$\Rightarrow \cos 30^{\circ}=\sqrt{\frac{1+\cos 60^{\circ}}{2}}=\sqrt{\frac{1+\frac{1}{2}}{2}}=\sqrt{\frac{\frac{3}{2}}{2}}=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}$

$\therefore \cos 30^{\circ}=\frac{\sqrt{3}}{2}$


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