SOLUTION: tgx + ctgx = -2

Let y = tg(x) be the new variable.


Then the given equation takes the form  

 = -2.


Multiply by y both sides. You will get

 = -2y,   or

 = 0,

 = 0  --->  y+1 = 0.


Hence, tg(x) + 1 = 0  --->  tg(x) = -1  --->  x =   and/or  x = .

Answer.  There are 2 solutions:  x =   and/or  x = .