Question

Мне докажите тождество: 4sin * cos (1-tg²) / 1+ tg² = sin 4

Answer 1

$\frac{4sin \alpha cos \alpha (1-tg ^{2} \alpha ) }{1+tg ^{2} \alpha } =$$\frac{4sin \alpha cos \alpha (1- \frac{sin ^{2} \alpha }{cos ^{2} \alpha }) }{ \frac{1}{cos ^{2} \alpha } } =4sin \alpha cos \alpha * \frac{cos ^{2} \alpha -sin ^{2} \alpha }{cos ^{2} \alpha } *cos ^{2} \alpha =$

$=4sin \alpha cos \alpha (cos ^{2} \alpha -sin ^{2} \alpha )=2sin2 \alpha cos2 \alpha =sin4 \alpha$