Question

упростить выражение(любое из двух)​

Answer 1

$1)frac{32cosa*sina*cos2a*cos4a*cos8a}{sin16a}=frac{16(2sinacosa)cos2a*cos4a*cos8a}{sin16a}=\\=frac{16sin2a*cos2a*cos4a*cos8a}{sin16a}=frac{8(2sin2a*cos2a)*cos4a*cos8a}{sin16a}=\\=frac{8sin4a*cos4a*cos8a}{sin16a}=frac{4(2sin4a*cos4a)*cos8a}{sin16a}=\\=frac{4sin8a*cos8a}{sin16a}=frac{2(2sin8a*cos8a)}{sin16a}=frac{2sin16a}{sin16a}=2$

$frac{cos3a*cos6a*cos12a*cos24a}{sin48a}=frac{cos3a*cos6a*cos12a*cos24a}{2sin24a*cos24a}=frac{cos3a*cos6a*cos12a}{2sin24a}=\\=frac{cos3a*cos6a*cos12a}{2*2sin12a*cos12a}=frac{cos3a*cos6a}{4sin12a}=frac{cos3a*cos6a}{4*2sin6a*cos6a}=frac{cos3a}{8sin6a}=\\=frac{cos3a}{8*2sin3a*cos3a}=frac{1}{16sin3a}$