Tan squared plus sec squared: 1+tan? θ = seconds? θ, this formula is listed as one of the square relations in the old high school mathematics textbooks. The derivative of tanx is sec? The derivative of x and secx is Tanxsecx, and tan stands for tangent. Angle θ In any right triangle, the ratio of the opposite side to the adjacent side corresponding to θ is called the tangent of angle θ. If θ is placed in a rectangular coordinate system, that is, tan θ = y/x. TanA= opposite side/adjacent side. Equivalent to the slope k of a straight line in a rectangular coordinate system. The tangent theorem is that in a plane triangle, the quotient obtained by dividing the sum of any two sides by the difference between the first side and the second side is equal to the tangent of half the sum of the diagonals of these two sides divided by the tangent of the difference between the diagonals of the first side and the second side.