How do you simplify using the sum and difference formula ##tan(285)##?
February 20th, 2023
##-(2+sqrt3)##.
##tan285^@=tan(360^@-75^@)=-tan75^@=-tan(45^@+30^@)##
##=-{(tan45^@+tan30^@)/(1-tan45^@*tan30^@)}##
##=-{(1+1/sqrt3)/(1-1/sqrt3)}##
##=-{(sqrt3+1)/(sqrt3-1)}##
##=-{(sqrt3+1)/(sqrt3-1)*(sqrt3+1)/(sqrt3+1)}##
##=-(sqrt3+1)^2/2##
##=-1/2(3+2sqrt3+1)##
##=-(2+sqrt3)##.
