Предмет: Математика, автор: vrschk

помогите!!!!!!.......

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Ответы

Автор ответа: Аноним

Покрокове пояснення:

$sin^4(\alpha )+sin^2(\alpha )cos^2(\alpha )+cos^2(\alpha ) = sin^4(\alpha )+cos^2(\alpha )*(sin^2(\alpha )+1);$

$sin^2(\alpha )+cos^2(\alpha )=1;\\$

$sin^4(\alpha )+cos^2(\alpha )*(sin^2(\alpha )+1)=\\=sin^4(\alpha )+cos^2(\alpha )*(sin^2(\alpha )+sin^2(\alpha )+cos^2(\alpha ))=\\=sin^4(\alpha )+cos^2(\alpha )*(2sin^2(\alpha )+cos^2(\alpha ))=\\=sin^4(\alpha )+2cos^2(\alpha )*sin^2(\alpha )+cos^4(\alpha )=\\=(sin^2(\alpha )+cos^2(\alpha ))^2=\\=(1)^2=1$

Б)

$\frac{sin^2(\beta )-1}{cos^2(\beta )-1} +ctg(\beta )tg(\beta )=\\=\frac{sin^2(\beta )-(sin^2(\beta )+cos^2(\beta ))}{cos^2(\beta )-(sin^2(\beta )+cos^2(\beta ))} +\frac{cos(\beta )*sin(\beta )}{sin(\beta )*cos(\beta )} =\\=\frac{-cos^2(\beta )}{-sin^2(\beta )} +1=\frac{cos^2(\beta )}{sin^2(\beta )}+1=ctg^2(\beta )+1=\\=\frac{1}{sin^2(\beta )}$