2006 Cyprus Seniors Provincial/2nd grade/Problem 3
Problem
If $\Alpha=\frac{1-cos\theta}{sin\theta}$ (Error compiling LaTeX. Unknown error_msg) and $\Beta=\frac{1-sin\theta}{cos\theta}$ (Error compiling LaTeX. Unknown error_msg), prove that $\frac{\Alpha^2}{(1+\Alpha^2)^2} + \frac{\Beta^2}{(1+\Beta^2)^2} = \frac{1}{4}$ (Error compiling LaTeX. Unknown error_msg).
