ABSTRACT
I f Equation 1 is not particularly remarkable, an immediate conse-
quence of it certainly is: I f we substitute x = we get
l - l = I t a n f + i t a n ^ + § t a n £ + . . .
Replacing the 1 on the left side with tan \ , moving all the tangent terms
to the right side and dividing the equation by 4, we get
i = ¿ t a n f + | t a n f + ¿ t a n ^ + . . . (2)
Equation 2 must surely rank among the most beautiful in all of math-
ematics, yet it does not appear in trigonometry or calculus textbooks;
nor is it listed in L . B . W . Jolley's Summation of Series [Jol61], a compi-
lation of over a thousand arithmetic, algebraic, and trigonometric series.
