Докажете тъждеството

[Paincho]

Здравейте. Може ли малко помощ за следните задачи:
1)[tex]1-tg^{2}\alpha . tg^{2}\beta = \frac{cos(\alpha+\beta)cos(\alpha-\beta) }{cos^{2}\alpha cos^{2}\beta }[/tex]
2)[tex]\frac{sin2\alpha}{cotg\frac{\alpha}{2} - tg\frac{\alpha}{2}} = sin^{2}\alpha[/tex]

Благодаря предварително.

[strangerforever]

1)[tex]1-tg^{2}\alpha . tg^{2}\beta = \frac{cos(\alpha+\beta)cos(\alpha-\beta) }{cos^{2}\alpha cos^{2}\beta }[/tex]

[tex]\frac{cos^{2}\alpha.cos^{2}\beta - sin^{2}\alpha.sin^{2}\beta}{cos^2\alpha.cos^2\beta} = \frac{cos(\alpha+\beta)cos(\alpha-\beta) }{cos^{2}\alpha cos^{2}\beta }[/tex]

[tex]cos^{2}\alpha.cos^{2}\beta - sin^{2}\alpha.sin^{2}\beta = cos(\alpha+\beta)cos(\alpha-\beta)[/tex]

[tex]cos^{2}\alpha.cos^{2}\beta - sin^{2}\alpha.sin^{2}\beta = (cos\alpha.cos\beta - sin\alpha.sin\beta)(cos\alpha.cos\beta + sin\alpha.sin\beta)[/tex]

[tex]cos^{2}\alpha.cos^{2}\beta - sin^{2}\alpha.sin^{2}\beta = cos^{2}\alpha.cos^{2}\beta - sin^{2}\alpha.sin^{2}\beta[/tex]