Prima data, folosesti formula:
[tex] \boxed{cos(2 \alpha) = cos \ \alpha ^2 - sin \ \alpha ^2} [/tex]
[tex] cos(2 arctg \ a) = \\ = cos( arctg \ a) ^2 - sin(arctg \ a)^2 [/tex]
Acum folosesti formulele:
[tex] \boxed{cos(arctg \ \alpha) =\dfrac{1}{\sqrt{1+ \alpha ^2}}} \\ \boxed{sin(arctg \ \alpha) =\dfrac{\alpha}{\sqrt{1+ \alpha ^2}}} [/tex]
Continuam folosind aceste formule:
[tex] \left( \dfrac{1}{\sqrt{1+a^2}} \right)^2 -\left( \dfrac{a}{\sqrt{1+a^2}} \right)^2 \\ = \dfrac{1}{a^2 +1} - \dfrac{a}{a^2 +1} \\ = \tt \dfrac{1-a^2}{a^2+1} [/tex]
