Question

cos4α * tg2α - sin4α = -tg2α доведіть тотожість !!!

Answer 1

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