Difference between revisions of "2006 Cyprus Seniors Provincial/2nd grade/Problem 3"
m (space) |
m (.) |
||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
If <math>\Alpha=\frac{1-cos\theta}{sin\theta}</math> and <math>\Beta=\frac{1-sin\theta}{cos\theta}</math>, prove that | If <math>\Alpha=\frac{1-cos\theta}{sin\theta}</math> and <math>\Beta=\frac{1-sin\theta}{cos\theta}</math>, prove that | ||
| − | <math>\frac{\Alpha^2}{(1+\Alpha^2)^2} + \frac{\Beta^2}{(1+\Beta^2)^2} = \frac{1}{4}</math> | + | <math>\frac{\Alpha^2}{(1+\Alpha^2)^2} + \frac{\Beta^2}{(1+\Beta^2)^2} = \frac{1}{4}</math>. |
Revision as of 10:53, 11 November 2006
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).
