cos(x+y)=cos x cos y - sin x sin y" " " " " "cos(x+y)=cosxcosy−sinxsiny 1st equation
cos(x-y)=cos x cos y+sin x sin y" " " " " "cos(x−y)=cosxcosy+sinxsiny 2nd equation
Add first and second equations
cos(x+y)+cos(x-y)=2*cos x cos y+0cos(x+y)+cos(x−y)=2⋅cosxcosy+0
cos(x+y)+cos(x-y)=2*cos x cos ycos(x+y)+cos(x−y)=2⋅cosxcosy
and then
cos x cos y=1/2[cos(x+y)+cos(x-y)]cosxcosy=12[cos(x+y)+cos(x−y)]
Let x=(5pi)/6x=5π6 and y=pi/6y=π6
cos((5pi)/6)*cos(pi/6)=1/2[cos((5pi)/6+pi/6)+cos((5pi)/6-pi/6)]cos(5π6)⋅cos(π6)=12[cos(5π6+π6)+cos(5π6−π6)]
cos((5pi)/6)*cos(pi/6)=1/2[cos pi+cos ((2pi)/3)]=1/2(-1-1/2)=-3/4cos(5π6)⋅cos(π6)=12[cosπ+cos(2π3)]=12(−1−12)=−34
God bless America ....