Question 396492
Since all coterminal angles have the same trig values, we can subtract 2pi, so:


{{{cot (31pi/12) = cot(7pi/12) = 1/tan(7pi/12)}}}


You can compute {{{tan(7pi/12)}}} without using a calculator, using the addition formula {{{tan (alpha + beta) = (tan (alpha) + tan(beta))/(1 - tan(alpha)tan(beta))}}}, and letting {{{alpha = pi/4}}}, {{{beta = pi/3}}}. You can then substitute those values in. I don't have enough time now, so I'll have you give it a try! Don't forget to invert your answer since you're looking for the cotangent, not the tangent.