Using the formula,cos A=√1+cos2A/2, find the value of cos 30°,it being given that cos 60°=1/2

Using the formula,cos A=√1+cos2A/2, find the value of cos 30°,it be

1.	Using the formula,cos A=√1+cos2A/2, find the value of cos 30°,it being given that cos 60°=1/2
Answer» Given formula : cos A =\xa0{tex}\\sqrt{1}{/tex}\xa0+\xa0{tex}\\frac {cos2A}{2}{/tex}Also, cos60 = {tex}\\frac {1}{2}{/tex}Required to find : cos30Now,Let A = 30o, 2A = 60ocosA =\xa0{tex}\\sqrt{1}{/tex}\xa0+ {tex}\\frac {cos2A}{2}{/tex}cos30=\xa0{tex}\\sqrt{( } 1+1 / 2) / 2{/tex}cos30 =\xa0{tex}\\sqrt{( } 3 / 2) / 2{/tex}cos30 =\xa0{tex}\\sqrt {(\\frac {3}{4})} =\\sqrt \\frac {3}{2}{/tex}\xa0Therefore,\xa0{tex}\\cos 30=\\frac{\\sqrt{3}}{2}{/tex}