Question 758678
we rewrite:
{{{
tanx+cotx = sin(x)/cos(x)+sin(x)/cos(x)
}}}


{{{
tanx+cotx=1/(sin(x)cos(x))
}}}


Next we can square the given equation:

{{{
sin(x)+cos(x) = 1/2}}} 

to get...

{{{
sin^2(x)+2sin(x)cos(x)+cos^2(x) = 1/4
}}}


and after simplifying we get
{{{sin(x)cos(x)=-3/8}}}



which means


{{{
tanx+cotx=-8/3
}}}