(1-cos^2a) / (1+tg^2 a)

$\frac{1-cos ^{2} \alpha }{1+ tg^{2} \alpha } =(1- cos^{2} \alpha ): \frac{1}{ cos^{2} \alpha } = sin^{2} \alpha * cos^{2} \alpha =(sin \alpha *cos \alpha ) ^{2} =$
$= ( \frac{1}{2}*2*sin \alpha *cos \alpha )^{2} = ( \frac{1}{2} )^{2}*(2sin \alpha cos \alpha ) ^{2} = \frac{1}{4} * sin^{2} 2 \alpha =$
=0,25*sin²2α

вариант условия 2. знак умножения:
(1-cos²α)*(1+tg²α)=sin²α*(1/cos²α)=sin²α/cos²α=(sinα/cosα)²=tg²α