Question 1126353
{{{tan(x)+cot(x) = 2/sin(x)}}}


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


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


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


since {{{sin(2x) = 2 sin(x) cos(x)}}}


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

So


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


Your original premise was wrong, a typo, missing the sin(2x)


*[illustration tan].

I graphed the 2 equations, and you see, they are the same. When doing this type of problem, graphing provides a nice way to check work.