Question 890116
{{{sin (theta) + cos(theta) = sqrt(3)}}}
==> {{{(sin(theta))^2 + 2sin(theta)*cos(theta) + (cos(theta))^2 = 3}}}, after squaring both sides.

==> {{{1 + 2sin(theta)*cos(theta) = 3}}}  (why?)
==>  {{{ sin(theta)*cos(theta) = 1}}}.

Now {{{tan(theta) + cot(theta) = sin(theta)/cos(theta) + cos(theta)/sin(theta) = ((sin(theta))^2 + (cos(theta))^2)/(sin(theta)*cos(theta)) = 1/(sin(theta)*cos(theta)) = 1/1 = 1}}}