#"using the "color(blue)"trigonometric identities"#
#•color(white)(x)sin(x+y)=sinxcosy+cosxsiny#
#•color(white)(x)cos(x+y)=cosxcosy-sinxsiny#
#"note that "(5pi)/12=pi/4+pi/6#
#rArrsin((5pi)/12)=sin(pi/4+pi/6)#
#rArrsin(pi/4+pi/6)#
#=sin(pi/4)cos(pi/6)+cos(pi/4)sin(pi/6)#
#=(1/sqrt2xxsqrt3/2)+(1/sqrt2xx1/2)#
#=sqrt3/(2sqrt2)+1/(2sqrt2)#
#=(sqrt3+1)/(2sqrt2)xxsqrt2/sqrt2=1/4(sqrt6+sqrt2)larrcolor(red)"exact value"#
#cos((5pi)/12)=cos(pi/4+pi/6)#
#rArrcos(pi/4+pi/6)#
#=cos(pi/4)cos(pi/6)-sin(pi/4)sin(pi/6)#
#=(1/sqrt2xxsqrt3/2)-(1/sqrt2xx1/2)#
#=(sqrt3-1)/(2sqrt2)xxsqrt2/sqrt2#
#=1/4(sqrt6-sqrt2)larrcolor(red)"exact value"#
#tan((5pi)/12)=sin((5pi)/12)/cos((5pi)/12)#
#color(white)(xxxxxxx)=(sqrt6+sqrt2)/(sqrt6-sqrt2)xx(sqrt6+sqrt2)/(sqrt6+sqrt2)#
#color(white)(xxxxxxx)=(6+2sqrt12+2)/4#
#color(white)(xxxxxxx)=(8+4sqrt3)/4#
#color(white)(xxxxxxx)=2+sqrt3larrcolor(red)"exact value"#
