rarrtan(1/2(sin^(-1)(1/2))
=tan(30^@/2) or tan(150^@/2)
=tan15^@ or tan75^@
Now, rarrtan15^@
=tan(45^@-30^@)
=(tan45^@-tan30^@)/(1+tan30^@tan45^@)
=(1-(1/sqrt3))/(1+1/sqrt3)
=(sqrt3-1)/(sqrt3+1)xx(sqrt3-1)/(sqrt3-1)
=((sqrt(3))^2-2sqrt3+1^2)/((sqrt3)^2-1^2)=(4-2sqrt3)/2=2-sqrt3
Similary, rarrtan75^@
=tan(45^@+30^@)
=(tan45^@+tan30^@)/(1-tan30^@tan45^@)
=(1+(1/sqrt3))/(1-1/sqrt3)
=(sqrt3+1)/(sqrt3-1)xx(sqrt3+1)/(sqrt3+1)
=((sqrt(3))^2+2sqrt3+1^2)/((sqrt3)^2-1^2)=(4+2sqrt3)/2=2+sqrt3