Question

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

Answer 1

LHS=`(1-sin 60^0)/(cos 60^0) =(1-(sqrt(3))/2)/(1/2) = (((2-sqrt(3))/2))/(1/2) =((2-sqrt(3))/2) xx2=2-sqrt(3)`

RHS=`(tan60^0-1)/(tan60^0+1) = (sqrt(3)-1)/(sqrt(3)+1) = (sqrt(3)-1)/(sqrt(3)+1) xx(sqrt(3)-1)/(sqrt(3)+1)=((sqrt(3)-1)^2)/((sqrt(3))^2-1^2)=(3+1-2sqrt(3))/(3-1) =(4-2sqrt(3) )/2 = 2-sqrt(3)`

Hence, LHS = RHS

`∴ (1-sin 60^0)/(cos 60^0)=(tan 60^0-1)/(tan60^0+1)`