If cos (pi/6) = (sqrt 3/2), how can I find cos (pi/12) using a double angle formula?

1 Answer
Dec 2, 2017

cos(pi/12)=1/2sqrt(sqrt3+2)

Explanation:

"using the "color(blue)"double angle formula"

•color(white)(x)cos2A=2cos^2A-1

cos(2xxpi/12)=2cos^2(pi/12)-1

rArrcos(pi/6)=2cos^2(pi/12)-1

rArrcos^2(pi/12)=1/2(cos(pi/6)+1)

color(white)(rArrcos^2(pi/12))=1/2(sqrt3/2+1)

color(white)(rArrcos^2(pi/12))=1/4(sqrt3+2)

rArrcos(pi/12)=sqrt(1/4(sqrt3+2)

color(white)(rxxxxxxxx)=1/2sqrt(sqrt3+2)larrcolor(red)"exact value"