We have

` "LHS " = (sin^(3) theta + cos ^(3) theta)/(sin theta+ cos theta )+ sin theta cos theta `

` = ((sin theta+ cos theta)(sin^(2) theta+ cos ^(2) theta- sin theta cos theta))/((sin theta + cos theta ))+ sin theta cos theta `

` [ because (a^(3)+b^(3))=(a+b)(a^(2)+b^(2)-ab)] `

` =(1- sin theta cos theta)+ sin theta cos theta=1 " " [ because sin^(2) theta+ cos^(2) theta =1] `

`= "RHS. "`

` therefore " LHS "= "RHS. " `