Solve the equation cot 2x + cot x = 3

tan2x*cotx - 3 = 0

We know that: tan2x = sin2x/cos2x and cotx = cosx/sinx

==> sin2x/cos2x * cosx/sinx = 3

Now we know that sin2x = 2sinx*cosx

==> 2sinxcosx/cos2x * cosx/sinx = 3

Reduce sinx:

==> 2cos^2 x / cos2x = 3

Now we know that cos2x = 2cos^2 x-1

==> 2cos^2 x / (2cos^2 x - 1) = 3

==> 2cos^2 x = 3 (2cos^2 x - 1)

==> 2cos^2 x = 6cos^2 x - 3

==> - 4cos^2 x = - 3

==> 4cos^2 x = 3

==> cos^2 x = 3/4

==> cosx = + - sqrt3 / 2

==> x = pi/6, 5pi/6, 7pi/6, and 11pi/6