Question

упростить выражение(любое из двух)​

Answer 1

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

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