Question

using the formula,cosA = √{(1+cos 2A)/2}, find the value of cos 30°, it being given that cos 60° = 1/2

​

Answer 1

please see the attachment

Answer 2

Given :

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

To find : $\cos 30^\circ=?$

Solution :

$\cos 30^\circ=\sqrt{\dfrac{1+\cos 60^\circ}{2}}\\\\\cos 30^\circ=\sqrt{\dfrac{1+\dfrac{1}{2}}{2}}\\\\\cos 30^\circ=\sqrt{\dfrac{1+0.5}{2}}\\\\\cos 30^\circ=\sqrt{\dfrac{1.5}{2}}\\\\\cos 30^\circ=0.866$

Hence, the value of cos 30° =  0.866.