Тригонометрия

[ivana123]

cos4[tex]\alpha[/tex].tg2\alpha-sin4\alpha={2tg\alpha \choose tgx^{2}\alpha-1}

[S.B.]

$cos4\alpha.tg2\alpha-sin4\alpha= \frac{2tg\alpha}{tg^{2}\alpha - 1}$

Предполагам,че така изглежда равенството,което(според мен!) трябва да се докаже

Доказателство:
[tex]cos4\alpha.tg2\alpha - sin4\alpha =[/tex]

$ = cos4\alpha.\frac{sin2\alpha}{cos2\alpha} - sin4\alpha = \frac{cos4\alpha.sin2\alpha - sin4\alpha.cos2\alpha}{cos2\alpha} = \frac{- sin2\alpha}{cos2\alpha} = - tg2\alpha = - \frac{2tg\alpha}{1 - tg^{2}\alpha} = $

$= \frac{2tg\alpha}{tg^{2}\alpha - 1}$