Find exact value of #cos(pi/12)#?

1 Answer

Answer:

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

Explanation:

According to the law of fractional angle,
#costheta=2cos^2(theta/2)-1#
In this form we can write,
#cos(pi/6)=2cos^2(pi/12)-1#
#=>sin(pi/2-pi/6)=2cos^2(pi/12)-1#
#sin(pi/3)=2cos^2(pi/12)-1#
#sqrt3/2+1=2cos^2(pi/12)#
#cos^2(pi/12)=(2+sqrt3)/2# and

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

= #sqrt((4+2sqrt3)/4)#

= #sqrt(((sqrt3)^2+2sqrt3+1^2)/4)#

= #(sqrt3+1)/2#