Question

Докажите тождество, срочно!

Answer 1

$\frac{4\, sin^4\frac{a}{4}}{1-cos^2\frac{a}{2}}=\frac{4\, sin^4\frac{a}{4}}{sin^2\frac{a}{2}}=\frac{4\, sin^4\frac{a}{4}}{(sin(2\cdot \frac{a}{4}))^2}=\frac{4\, sin^4\frac{a}{4}}{(2\, sin\frac{a}{4}\cdot cos\frac{a}{4})^2}=\frac{4\, sin^4\frac{a}{4}}{4\cdot sin^2\frac{a}{4}\cdot cos^2\frac{a}{4}}=\\\\=\frac{sin^2\frac{a}{4}}{cos^2\frac{a}{4}}=tg^2\frac{a}{4}$