Question

Show that `(cos 30^circ + sin 60^circ)/(1 + sin 30^circ + cos 60^circ) = cos 30^circ`.

Answer 1

LHS =`(cos30^0+sin 60^0)/(1+sin30^0+cos60^0) = ((sqrt(3)/2+sqrt(3)/2))/(1+1/2+1/2)=((sqrt(3)+sqrt(3))/2)/((2+1+1)/2)=sqrt(3)/2`

Also, RHS = cos `30^0=sqrt(3)/2`

Hence, LHS = RHS

∴`(cos30^0+sin 60^0)/(1+sin30^0+cos60^0)=cos 30^0`