Question Detail

cot(π/4 - t) = 1/tan(π/4 - t). Using tangent subtraction formula: tan(π/4 - t) = (tan(π/4) - tan t)/(1 + tan(π/4) tan t) = (1 - 13)/(1 + 13) = (-12)/14 = -6/7. Therefore cot(π/4 - t) = -7/6 ≈ -1.1667. Option C is -1/13 ≈ -0.0769, which is not matching. Using cot(π/4 - t) = (1 + tan t)/(tan t - 1) = (1+13)/(13-1) = 14/12 = 7/6, positive.