Question

If 3cot^2 x - 5cotx = -2, then cotx = _____.

Answer 1

Hint: First rewrite it as \(3\cot^2 x - 5\cot x + 2 =0\). Then note that this is a qudratic function in \(\cot x\); that means, if we were to make the substitution \(t=\cot x\), the equation would turn into \(3t^2-5t+2 =0\), which can be factored and solved for \(t\). Once you solve for t, then substitute back \(\cot x\) and solve for x.

Do you think you can take things from here? Or should I show a few steps as to what I mean by this? :-)